F3G,
I believe, strongly, that, carried out carefully and professionally, the benefits of feedback surveys would outweigh the risk.
W.r.t. the confidence flying schools have in their training operations, this is my point precisely: many seem to wish to give the impression that they are not confident in their product.
(Whilst the quality of training is the paramount issue, how often does one see badly worded, or insufficiently detailed, 'promotional' material {either printed, or upon the WorldWideWeb}, insalubrious reception areas, obsolete equipment left in situ, an attitude amongst desk staff that the casual enquirer should 'know what to ask for', etc., etc.? These matters all militate against the student, and, in particular, the potential customer, regarding the training to be had as of high quality.)