The car only takes BLE readings when the car is moving, generally. I suppose it can happen right when you're pulling into the garage, but if it's reading 20psi while driving, it has nothing to do with the stored set.
I've got a set of BLE sensor-equipped wheels about 3 feet from my Tesla and it doesn't affect anything. If your car is parked, it's not taking pressure measurements.
Remember, you can park RIGHT next to another Tesla in a parking lot, (Inches away wheel-to-wheel) and it won't grab the sensor data from the other car.
If it's reading 20psi while driving, go into Service Mode and reset the "Learned Tire Values" under the Chassis tab. If that doesn't fix it, you might have a bad sensor. It's happened to a few users on this forum, not completely unheard of.