The Correct Response is, of course, correct. The time dilation affect must affect half-lives (which are measured in units of time) or else relativity would be invalid.
But, a warning.... to understand what this means... you need to understand the key principle of Relativity; there are more than one points of view, and they are equally correct.
Take a the proposed decaying substance (which from your point of view is moving very very fast). From your point of view, the substance would decay slower than it should... which makes sense given our understanding of time dilation.
Of course to a person who is sitting on the substance... the substance isn't moving at all (although the Earth and the solar system are hurtling toward them very very fast). To this observer the substance would decay at exactly the "correct" rate, although they would measure the distance between the Earth and the substance as shorter than the original observer.
If you are holding the substance in your hand... then time dilation due to speed has nothing to do with any measurement you might make (no matter how fast some other observer thinks you are moving).
This has been observed by very fast particles which are created at the top of our atmosphere and make it much farther down then they should (given that they should decay before they travel that far).