You are correct that LimeLM is behaving as designed.
The problem is with Paypal's "sandbox" (testing) environment.I spoke to one of their support people, and he explained to me that the email accounts that get set up in their sandbox environment are not fully functional, and that causes the payments to get flagged as "Pending" instead of "Complete".
He said that I would have to test it in my "live" Paypal environment, with a real email account, in order to get the transaction to complete.
So, beware Paypal users -> the Paypal sandbox environment is not capable of testing a "Complete" transaction for the purposes of LimeLM / TurboActivate!