It looks like you are not using 'use strict' in your script, if you did you would get errors as 'true' and 'false' have no special meaning in Perl:

use strict;
use warnings;
my %groups = (
    'GroupID1' => true,
    'GroupID2' => false
);
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Errors:

Bareword "true" not allowed while "strict subs" in use
Bareword "false" not allowed while "strict subs" in use
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Your hash will be turned into a JSON structure before it is sent to MailChimp, and the way to represent JSON true and false in a Perl hash is:

my %groups = (
    'GroupID1' => \1,
    'GroupID2' => \0
);
[download]

Maybe try that and see.