Maybe the person who told you residents pay tuition wasn't from the USA? In Canada, residencies are part the post-grad medical education office of universities. At some schools, you do have to pay some tuition but it isn't much.
Nah, its not a touchy subject its just that the others here forget how ignorant they once were and like to pounce on the newbies.
Don't worry about it. Residents in the US, at accredited programs do not pay tuition. Besides the Canadian programs, every now and again you hear about an FMG who pays a US program for a residency; this may also be what your source was referring to.