OK, that explains it. (I had an incorrect mental model: I was thinking that <FH> always put the data somewhere, using $_ unless otherwise specified. I don't know how I came to think that, as in hindsight that would be clearly stupid. Oh, well--live and learn!)

So the correct fix to my program would is to change the inner loop from:

  for my $cnt (0 .. 3) {
     my $t=<DATA>;
     print $t;
  }
[download]

to

  for my $cnt (0 .. 3) {
     $_=<DATA>;
     print;
  }
[download]

so I can avoid unnecessary variables and clutter.

Thank you!