Brake fluid is hydroscopic. It absorbs moisture. Thats why you are supposed to change it.
I wouldn't expect the brake fluid to cause a lock up - quite the opposite as the more water in the fluid, the lower the boiling point and then you get brake fade on heavy braking.
Also stops cylinders/calipers corroding if you change it regularly.

I'd agree with the tyre theory - but change your fluid anyway!!