This answer repeats some of the material in other answers but I think it is not entirely redundant.

As you seem to have realized, the assertion that a theory is consistent is a <i>much</i> weaker statement than the assertion that the theory does not prove false arithmetical statements (or is "arithmetically sound", to use the standard terminology). So the answer to your question about whether it could be the case that ZFC + universes is consistent but not arithmetically sound is yes, but for perhaps a trivial reason: ZFC + universes could be consistent and yet ZFC itself could fail to be arithmetically sound.  Probably what you really wanted to ask was, if ZFC is arithmetically sound, and ZFC + universes is consistent, does it follow that ZFC + universes is arithmetically sound?  The answer is no.  For example, it is conceivable that under these hypotheses, ZFC + universes could prove $\neg$Con(ZFC). (<b>EDIT:</b> This was a typo. I meant that ZFC+universes could prove $\neg$Con(ZFC+universes). Thanks to Noah Schweber for catching this&mdash;see the comments.)


Any feeling that universes are a "safe" assumption must come from a direct assessment of the universes axiom itself.  The reasons are similar to the reasons that we have for believing that ZFC is arithmetically sound.

The ability to remove Grothendieck universes from the proof of Fermat's Last Theorem cannot be deduced from some simple abstract fact like "Fermat's Last Theorem has low quantifier complexity."  No meta-theorem of this sort is known. Eliminability must come from careful examination of the nitty-gritty details of the proof.

Your question about whether Con(PA) is philosophical or mathematical needs clarification.  Offhand, it sounds like a false dichotomy to me, predicated on dubious assumptions about the meaning of the words "philosophical" and "mathematical." Can you define precisely what you mean by a "mathematical" assumption?  Are you implicitly assuming that "mathematical" assumptions are rock-solid while "philosophical" ones are not?  If so, that in itself is a dubious assumption IMO.