When ppl ask does it matter, my opinion is that this is a two-fold issue. Does it matter in terms of your training and ability to be a
competent/sound dentist and professor? I sincerely doubt that it does.
On the other hand if you think academia is free from such concerns as prestige you're hoping for a world that isn't this one. It definitely
does make it easier to be selected for a position in academia if you have a pedigreed background. You can still do it without that pedigree but
it is easier.
That said I think the point ppl are usually trying to make is that you can do whatever you want from virtually any situation. If the OP for example went
to MUSC and got involved in research, worked with good professors and had several publications, eventually their accomplishments would create the resume
that would overshadow any valuations ascribed to the school he/she attended.
In any walk of life if you've made the cut for a more prestigious or well-regarded job/position you become more valuable to most other organizations.
If you work at Google numerous startups will want you for your experience and perception that you know how the big guns do it. Same thing happens in residencies: if you train at some of the historically great and well reputed programs other programs will want to snap you up to raise the perception and possibly actual skill of their programs.
Feel free to disagree.