Solved! Go to Solution.
I tested it today and found that if you select a test lead record during the test send, then the forward link works. Otherwise it does not.
Apparently Marketo needs to attribute the forwarding action to a record in the lead database. This means that if a test is forwarded, the forward action may not be attributed to the person who forwarded, but to the person whose record was used to create the test email. Therefore it is better to have the people who will forward the email receive the production emails rather than tests.