I believe it wasn't that they 'couldn't use their license,' but that the license isn't exported (not in the list) for backup in the free version.
If they had registered on the avast web site not through the avastUI, then they would have received an email with the registration key, then they could use that if it still had time remaining. But that doesn't make much sense when you can get registered for a full year in under 30 seconds.
I don't know if the option to export the license is available in the paid versions as it makes more sense to back it up (so they don't lose the remaining period that they have paid for), but in the free version, you just quickly register on-line (through the avastUI) and your good to go for another year.