The Boeing 737 (300-900) FCTM reference is quite a recent change, they are now on Revision 9, dated 30 June 2010.
Edition 7 had the 'old' guidance as follows (cut & pasted):
Maintain wings level during the takeoff roll by applying control wheel displacement into the wind. During rotation continue to apply control wheel in the displaced position to keep the wings level during liftoff.
This was replaced in Revision 8, 31 October 2008, by the guidance given earlier, which is still the same in Revision 9:
Begin the takeoff roll with the control wheel approximately centered. Throughout the takeoff roll, gradually increase control wheel displacement into the wind only enough to maintain approximately wings level.
This shows that techniques are constantly under revision, and referring to FCTMs dated 1985 is probably not the best way to keep your skills up to date. Likewise referring to other machine's training guidance is not wise.
As for the statement "all airplanes fly the same", that is clearly rubbish, although a university professor in aeronautical physics may put it that way, because the fundamentals of lift/drag/thrust/weight/bernoulli etc do not change. They may all fly by the same principles of physics, but their handling qualities can be vastly different.