MIL with dementia claims to be engaged in activites she isn't. Is this common?

I agree-you can make the providers aware, but it's really not harming anyone if she's no longer got the capacity to do initiate and participate in what she used to. It's nice that she thinks she's still active. My mom does as well. If you want her to do some activities she'll need some kind of outside support to do them, and she may be at a point in her disease where not participating is her new comfort zone because she can't handle processing all the steps in an activity. If you feel like she needs to exercise maybe they could go for walks?

Yes often they can "work the system." It's called "show-timing." In your MIL's mind she truly believes that she is still doing theses things. That's part of dementia. I hope you don't argue with her about the fact that she no longer does those things, as it makes life much easier if you just go along with whatever she says. You may want to educate yourself a bit more about the disease so when these things come up you will already know that it's part of the disease.
But like Grandma1954 asked below, who is going to the doctor with her that she is allowed to put on such a show? Surely you're not letting her go by herself.
Someone should not only being going with her and IN with her, but should also be writing her doctor a note on the patient portal ahead of her appointment with everything that is going on with her, so they have a heads up before her appointment.
I had to do that all the time with my late husband, because if I didn't the doctor would ask him how things were going and my husband would always say fine. But in reality his doctor already knew that in fact things were not fine, and so things could be addressed.
It's such a simple solution for whoever is her medical POA or is on her HIPPA form. You can also just hand the nurse a note before your MIL is called back and she/he can hand it to the doctor before they come in the exam room.

Who is going to the doctor with her?
the person that is going to appointments with her should be informing the doctor about any changes, any declines, any other things that are going on.
If there are/is more than 1 caregiver they should ideally keep a log of what they are doing, what mom is doing and this should be brought with mom to appointments.
If no one is going with her how is she getting there?
(and when I mean "going with her" I do not mean driving her and waiting in the car or the waiting room)

Well, the answer to this is testing. Testing has to be done eventually in any case for staging and any tries at treatment. Confabulation is the most common thing in early and middle stages of some dementias, and yes, some can do very well indeed.

I am assuming you are mom's POA and her MPOA? Because a short and concise note to the MD such as you sent us is PERFECT for you to present when she goes for checkup. She should be seen for a diagnosis that is formal and written by a good neuro.

Meanwhile what you wrote tickled me. While many are sunk into depression and whining from a.m. to bedtime, your Mom is thinking she had a hole in one and a good lunch. It sounds delightful.

You mention "playing the system". I would say for those who are/were socially adept they are often the ones who love to put their best feet forward.

I sure wish you both the best.