Rick,
If the blade is an expensive one, look into a re-sharpening service. The machinist is right IMHO. On my band saw,I notice a definite tendency to wander as the blade gets hotter(due to dullness). Also, if the set of the teeth is gone, or favors one side, the blade will wander. If you go the re-sharpening route, have the blade's teeth set. This will usually happen during the sharpening.
You could also check to be sure that the guide blocks or bearings contact the blade properly, not too tight, supporting the blade near, but not touching, the back, or gullet of the teeth.
Hope this helps, Steve