It doesn't. Add a -Mstrict or use strict; and it complains.

$ perl -MO=Deparse,-p,-q 
use strict;

open my $fh, "<f1.txt" or do {
    print STDERR "can't open <f1.txt, but nevermind, I'll try f2.txt\n
+";
    open $fh, "<f2.txt" or die "still can't...";
};
print <$fh>;
^D

Global symbol "$fh" requires explicit package name at - line 5.
- had compilation errors.
use strict 'refs';
unless (open(my $fh, '<f1.txt')) {
    do {
        print(STDERR "can't open <f1.txt, but nevermind, I'll try f2.t
+xt\n");
        (open(${'fh'}, '<f2.txt') or die(q[still can't...]));
    };
}
print(<$fh>);
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