If you can't in general parse a piece of perl without "running the program" as you yourself mentioned then I'm pretty sure that parsing it can definitely trigger infinite loops as perl language is definitely turing complete during run time. So your statement is a contradiction.
The comment said you won't cause an infinite loop during parsing due to a bug in the language definition, not that you can't do so at all. Perl lets you run arbitrary code during parsing, so of course it's possible to run an infinite loop while parsing. But you can only do that by actually writing an infinite loop in your code, not by writing something that confuses the parser into looping forever.
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If you can't in general parse a piece of perl without "running the program" as you yourself mentioned then I'm pretty sure that parsing it can definitely trigger infinite loops as perl language is definitely turing complete during run time. So your statement is a contradiction.
The comment said you won't cause an infinite loop during parsing due to a bug in the language definition, not that you can't do so at all. Perl lets you run arbitrary code during parsing, so of course it's possible to run an infinite loop while parsing. But you can only do that by actually writing an infinite loop in your code, not by writing something that confuses the parser into looping forever.