I usually like to address this one with some question asking.
Okay, what dose does it take? How long is the immune system stimulated? Just what does it mean to be "stimulated"?
Usually the person can't answer those questions, they just know that radiation stimulates the immune system. Let's face it, if I introduce a pathogen into you it will stimulate your immune system, likewise if I cut you. That doesn't mean pathogens or cuts are good.
Okay, even if the immune system is "stimulated", how does the immune system (cells) get into the nuclei of other cells to repair the DNA damage that the radiation may have caused?
This may "stimulate" some thinking on their part, but don't expect it. Of course the immune system cells don't get into the nuclei. The immune system evolved to handle pathogens.
"But the immune system can attack cancer cells!", they'll exclaim.
Yes it can (because sometimes it recognizes cancer as a foreign pathogen) ! But if you've just had a dose of radiation and your immune system has been stimulated (highly variable), that effect is very short (hours to days). If DNA damage has occurred, it's occurred. And if cancer eventually manifests, it won't happen for many years down the road. There is no connection between any immune system response and carcinogenesis.
This is from the NAS's BEIR VII (emphasis mine):
The radiation-adaptive response in mammalian cells was demonstrated initially in human lymphocyte experiments (Olivieri and others 1984) and has been associated in recent years with the older concept of radiation hormesis. A more extensive treatment of adaptive effects is discussed in another section of this report. Radiation adaptation, as it was initially observed in human lymphocytes, is a transient phenomenon that occurs in some (but not all) individuals when a conditioning radiation dose lowers the biological effect of a subsequent (usually higher) radiation exposure. In lymphocyte experiments, this reduction occurs under defined temporal conditions and at specific radiation dose levels and dose rates (Shadley and others 1987; Shadley and Wiencke 1989). However, priming doses less than 5 mGy or greater than ~200 mGy generally result in very little if any adaptation, and adaptation has not been reported for challenge doses of less than about 1000 mGy. Furthermore, the induction and magnitude of the adaptive response in human lymphocytes is highly variable (Bose and Olivieri 1989; Hain and others 1992; Vijayalaxmi and others 1995), with a great deal of heterogeneity demonstrated between different individuals (Upton 2000). Also, the adaptive response could not be induced when the lymphocytes were given the priming dose during G0. Although inhibitor and electrophoretic studies suggest that alterations in transcribing messenger RNA and synthesis of proteins are involved in the adaptive response in lymphocytes, no specific signal transduction or repair pathways have been identified. A recent study (Barquinero and others 1995), which reported that chronic average occupational exposure of about 2.5 mSv per year over 7 to 21 years induced an adaptive response for radiation-induced chromosomal aberrations in human lymphocytes, also reported that the spontaneous level of aberrations was elevated significantly, presumably by the occupational exposure. (See Barquinero and others  for references to six other reports that basal levels of chromosome abnormalities are in general higher in exposed human populations.) These results suggest that occupational exposure may have induced chromosomal damage in the worker population while protecting lymphocytes from a subsequent experimental radiation exposure administered years after initiation of the chronic exposure. It is unclear whether such competing events would result in a net gain, net loss, or no change in health status.
In general, to observe hormetic effects the spontaneous levels of these effects have to be rather high. The committee notes in the Biology section that a very low radiation dose was reported to cause a reduction in transformation in vitro below a relatively high spontaneous transformation frequency. However, problems and possible artifacts of the assay system employed are also discussed. When radioresistance is observed after doses that cause some cell lethality—for example, after chronic doses that continually eliminate cells from the population—the radioresistance that emerges may be caused either (1) by some inductive phenomenon or (2) by selecting for cells that are intrinsically radioresistant. Either process 1 or process 2 could occur as the radiosensitive cells are selectively killed and thus eliminated from the population as the chronic irradiation is delivered. In the end, an adaptive or hormetic response in the population may appear to have occurred, but this would be at the expense of eliminating the sensitive or weak components in the population.
In chronic low-dose experiments with dogs (75 mGy/d for the duration of life), vital hematopoietic progenitors showed increased radioresistance along with renewed proliferative capacity (Seed and Kaspar 1992). Under the same conditions, a subset of animals showed an increased repair capacity as judged by the unscheduled DNA synthesis assay (Seed and Meyers 1993). Although one might interpret these observations as an adaptive effect at the cellular level, the exposed animal population experienced a high incidence of myeloid leukemia and related myeloproliferative disorders. The authors concluded that “the acquisition of radioresistance and associated repair functions under the strong selective and mutagenic pressure of chronic radiation is tied temporally and causally to leukemogenic transformation by the radiation exposure” (Seed and Kaspar 1992).
Back to the immune system attacking cancer, yes, sometimes the immune system can attack cancer. It sometimes sees it as a foreign body because it is genetically different than normal cells. And sometimes the cancer can evolve defense mechanisms against the immune system! After all, people with functioning immune systems get cancer! There's more info here, though it's a bit technical.
So bottom line....the radiation dose range to cause "stimulation" of the immune system is very narrow and the effect highly variable. It is a response to a biological insult (radiation), which goes away. If the dose is low and chronic (doesn't go away) we don't even see the effect. Immune response or not, some DNA is damaged by the radiation (and some repaired and mis-repaired). The immune system cells have no role in repairing DNA damage, they are separate cells. If a cancer eventually manifests it will happen far into the future relative to any immune response.
On top of all that, chronic inflammation (a chronic immune response) itself is linked to carcinogenesis! So even if you had some sort of long term immune system "stimulation", that doesn't mean the cancer risk would be expected to decrease.
(For even more info click on UNSCEAR's, Biological Effects Of Radiation, Annex D, Effects Of Ionizing Radiation On The Immune System).