It's because in the second instance you're looping over a constant value in the for and the trying to assign that in my_method e.g

sub readstuff { return while <> }
print readstuff for 'a constant value';

__output__

Modification of a read-only value attempted at - line 1.
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Where the while really compiles as return while defined($_ = <>). As has been mentioned before in IlyaM's while(<>) { ... } considered harmful, be careful when implicitly using $_ in subroutines and methods.
HTH

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broquaint