The trainer may not lie, but it's not infallible.
Last January, when I realized that I was spending some significant time on the trainer, I bought a wired speed and cadence sensor, primarily to keep track of miles and average speed. On the road, I had been using Map My Ride through the iPhone pretty faithfully. I had been calculating speed and distance on the trainer by multiplying my road average and perceived effort against time. Once I had the sensors and computer installed, my results suddenly dropped by about 3 miles per hour. Rats.
The Bianchi, which is now my back up bike, went back up on the trainer a month or so ago, but the speed and cadence has not been registering since a crash in mid July. The other day, I started to fiddle with it to line it back up, but then stopped myself. The three miles/hour I had lost last January had magically reappeared, simply by going back to the old methods. All is well.