> That He atom rapidly steals electrons from matter

tfa:

> Thanks to its filled outer electron shell, it is inert, and won’t react with other materials

The particle that is emitted from an alpha decay isn't actually called a He atom (I edited my root comment so this isn't misleading, apologies) -- I was being loose with terminology -- though it has the right number of protons and neutrons. It's called an alpha particle. Once it steals two electrons -- it carries a +2 charge and is extremely successfully at slicing electrons off of other molecules it comes across -- it is then considered the helium that we know and love, and is now stable with the properties we know.

And by stealing those electrons from other molecules it sets off other chemical reactions, which in things like DNA is highly suboptimal. This all generally happens at the birth of the He atom, presuming it isn't in deep space or something with no electrons to cleave from neighbours, and is only an instantaneous state.

Because it rapidly steals electrons, it becomes inert quickly. Helium you find lying around will be inert. Helium that has just shot out from the radioactive decay of an unstable atom will not be inert.