Suspicion that local repair shop swapped out Alzheimer's patient's Time Just for fake

[Caregiver]

Hi. I'm a caregiver and my client has Alzheimer's. The watch his mother got for him 40-50 years ago had something wrong with it so I took it to a local and well-respected watch repair shop who told me they were authorized to work on Rolex watches.
They charged my client over $1,000.00 to fix his classic Oyster Perpetual Time Just.
When it was finished 2 weeks later, I wasn't the one to go with him to pick it up, another caregiver was.

Now, three months later the watch is not working right. You can't change the time or the date and the date is wrong.

I went back to the same shop with my client and demanded an explanation. They said they would fix it again this time for free.

In the process, I had a chance to get a closer look at the watch and I'm suspicious that it's not the same original real Rolex and that they swapped it out with a fake.

I think the white dots and a couple other things give it away. Plus, I think it's lighter than his original watch. My client can't tell a difference (other than that it's not working right).

Help?