It doesn't matter if you use single, double, or no quotes. any of these are fine.

$ERRORS{CRITICAL}
$ERRORS{'CRITICAL'}
$ERRORS{"CRITICAL"}
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The error was that you forgot the '$', so perl was treating ERRORS as a subroutine invocation, and passing the hashref {"CRITICAL" => undef} as the argument.

You can verify that behaviour like this:

use Data::Dumper;
sub ERRORS {
    print "ERRORS called\n";
    print Dumper(\@_);
}

$a = ERRORS{"CRITICAL"};
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Which outputs:

ERRORS called
$VAR1 = [
          {
            'CRITICAL' => undef
          }
        ];
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By the way - in the future instead of saying "strict will puke" it would be better to provide the error.