This is a plausible scenario, I think the risk for the business is to great for someone to try this, for the business and for the user, in this situation pretty sure someone will try to scam people.
I guess many users will try this, but I wouldn't be surprised if some shitty exchanges would also try to make some extra profit from this opportunity.
There is an other scenario for "afterfork" scamming. I think if the "old" chain losing, and gets abandoned by most miners then it will be relative easy to take over and then this "privat chain" can be turned to a scammer hideout for selling freshly minted worthless coins to noobs.