"This might be a dumb question, but does your same_mod_time return 0 or 1 without the return?"

It returns TRUE or FALSE, i.e. whatever (stat($_[0]))[9] == (stat($_[1]))[9] evaluates to. In string context, that would be "1" or ""; in numeric context, that would be 1 or 0.

Modifying the test code I posted previously to demonstrate this:

$ > xxx 2> yyy
$ perl -Mstrict -Mwarnings -E '
    sub same_mod_time { (stat($_[0]))[9] == (stat($_[1]))[9] }
    say ">>>" . same_mod_time(qw{xxx yyy}) . "<<<";
'
>>>1<<<
$ perl -Mstrict -Mwarnings -E '
    sub same_mod_time { (stat($_[0]))[9] == (stat($_[1]))[9] }
    say 0 + same_mod_time(qw{xxx yyy});
'
1
$ > xxx
$ perl -Mstrict -Mwarnings -E '
    sub same_mod_time { (stat($_[0]))[9] == (stat($_[1]))[9] }
    say ">>>" . same_mod_time(qw{xxx yyy}) . "<<<";
'
>>><<<
$ perl -Mstrict -Mwarnings -E '
    sub same_mod_time { (stat($_[0]))[9] == (stat($_[1]))[9] }
    say 0 + same_mod_time(qw{xxx yyy});
'
0
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The presence or absence of the return keyword, in that subroutine, is immaterial. Here's what the doco says:

"return EXPR
...
Returns from a subroutine, eval, or do FILE with the value given in EXPR.
...
In the absence of an explicit return, a subroutine, eval, or do FILE automatically returns the value of the last expression evaluated. ..."