I had to read your post again, answer yes, if you have a single button fob then the alarm & c/l is a single unit and if the a key is used it operates a micro switch at the back of the drivers lock via plastic cam that break, or of course the alarm-C/L module could be faulty. First remove the door card to see whats happening.
With the two button fobs there are two seperate units now and the C/L actuator in the drivers do does the switching.