According to perlop, we are both sorta right:

The first time <> is evaluated, the @ARGV array is checked, and if it is empty, $ARGV[0] is set to "-", which when opened gives you standard input. The @ARGV array is then processed as a list of filenames.

So if there is nothing in @ARGV to begin with, it will read from STDIN. But as it reads from @ARGV, it unshifts the files from the array. So when the loop ends, $#ARGV = 0. But...

The <> symbol will return undef for end-of-file only once. If you call it again after this, it will assume you are processing another @ARGV list, and if you haven't set @ARGV, will read input from STDIN.

So it will return false once and then begin to read from STDIN.