Most of the time, if you addressed and invited only the recipient, it is understood that only they are invited to the wedding.
If you addressed and put on the invitation "and guest" then it is okay for that guest to invite a guest along.
Suggest to your friend that if these "single" guests happen to reply back with a guest added to their reply card number, she should contact them and explain honestly that with two families to accommodate, it was simply impossible to invite everyone you wanted to.
