The thing you said that someone disagreed with was calling it ionizing radiation, which is a more general term and describes radiation with enough energy to ionize an atom or molecule, which means stripping off at least one of its electrons. That requires a lot less energy than activating nuclei in an element that is not radioactive to radioactivity. UV light and X-rays are both ionising radiation, but are not from radioactivity and cannot induce radioactivity. Of course a lot of radioactive radiation (α, β, γ) is also too low-energy to activate more nuclei. It depends on the energy of the radiation and the specific element you're trying to activate (how close it is to being radioactive, so to speak).

So like CommissarVulpin said - the real danger is more likely to be contamination