in reply to <> and <ARGV> are the same thing, except when they aren't

Indeed, determining if what follows print is a file handle or not is very finicky. Since the parser always favours an expression to print over a handle, you can force unambiguity using curlies: 

print { $fh } ...;

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Note that contrary to what you said, indirect method calls are not affected, just the print operator. 

$ echo foo | perl -MCGI -e'new CGI <>;'

$

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Update: Last bit is wrong. 

$ perl -c -e'method $foo <>;'
syntax error at -e line 1, near "<>"
-e had compilation errors.

$ perl -c -e'method $foo <ARGV>;'
-e syntax OK

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In Section Meditations