"I am having" or "I have"?

I found this question in a test paper of an International English Competition. The task was to put the verb in brackets into the correct tense:

I can’t come. I _______ (have) piano lessons at that time.

The answer key says that the correct response would be:

I can’t come. I am having piano lessons at that time.

Is such an answer considered grammatically correct? If yes, why are we using the Present Progressive here instead of the Present Simple, which is used with schedules?

I can’t come. I have piano lessons at that time.

Is there an exception to this rule? I am totally stuck…