I had a similar problem with my car some 20 years ago. When I tried to apply the brakes, the brake pedal didn't move at all.
In this case, it was caused by a sloppy repair job when the wheel bearing was replaced. Somehow the sensor didn't properly align with the toothed ring after the repair, causing the controller to think the wheel was blocked.
The immediate remedy was to pull the ABS fuse (obviously that disabled the ABS for all wheels) until it could be repaired.
Long story short: you may want to check if the sensor is in the correct position. It it is, check the electrical connection and if that is okay as well, replace the ABS sensor. Or maybe check if the toothed ring is bent. If it's bent, the clearance between the ring and the sensor would vary, causing the controller to do strange things. Also check the teeth if they look normal.
I don't believe for one second that the tires could be the cause for this problem, but there is a chance that the shop bent the ring or otherwise caused trouble. It's certainly worth taking a look at.