There is no way to determine whether or not the complaint is real, in whole, or that the complaint is a 'either/or else' situation for the business owner. A harmless 'I don't like' comment from a customer does not mean that the customer will stop doing business. The owner is placed in the position of eliciting a qualifying statement from the customer, or to blow it off if the 'either/or else' statement is not made.
It would be nice to know which way the owner will go in that hypothetical situation.
Your continued employment is good.
The termination, if it happens, is bad, because the reason for termination could be held against you by a future employer. Even a simple termination for cause, or a some other uninformative response is still bad.
A future employer, hypothetically, would/could ask why you were terminated. There is no right answer other than the truth, you were terminated because you OC on your own time, because that is why you 'were' terminated.....wait, you quit, because you agreed to quit vs. being terminated. So, why did you quit? Once again, no right answer other than the truth, you OC in your off time.
Tough situation if it happens.
Good luck.