I'm no expert, but I don't think that bit of “common knowledge” is correct even though it certainly is a logical guess. As I understand it, they calculate the Doppler shift in the carrier signals coming from each satellite. Assuming that's the norm and not just ultra-expensive aviation units, then your GPS is probably more accurate than any other method at your disposal, and certainly more accurate than automotive speedometers. Try holding your speed constant on a long straight stretch of road and you will see that at a minimum your GPS yields very consistent and repeatable readings, and I suspect very accurate.
Edit: Garmin 60CS claims accuracy of 0.05 m/sec, which would be abut 1.7 inches per second. So unless your rowing team is REALLY slow, I think a GPS might be just the ticket.