Actually, class B AIS transponders have a built-in GPS that is always used. I believe that class A transponders can be set up with external location input and hence could - in theory at least - use recorded tracks.
It could also be a fault in the transponder. Last summer I noticed a boat that seemed to go 60 knots and have a very erratic location. This happened several days over a couple of weeks and I finally called him and he restarted the AIS, which cleared the problem. The coast guard had also made note of the problem, so it was not just my installation
On another occasion the GPS signal from my own AIS (an AMEC-101) sent out erratic data to OpenCPN causing the display of my own ship to be jumping all over the chart. I turned the AIS off and on and never saw the problem again.
m/v B.C. Girl.