Concur.
A checklist is a checklist whether or not you use a piece of paper or your memory.
Some of us here are getting confused with the challenge and response type of checklist as used in a multi-crew environemtn and a checklist used for single pilot ops.
The RAAF training system requires all normal (and bold faced emergency) checks be commited to memory, but pilots are also to carry a printed checklist for reference if needed.
I wouldn't have a problem with someone using a printed checklist if they were flying an aircraft they were unfamiliar with. However I would recommend that they take the next step and commit the checks to memory if they planned on using that aircraft type more often.
Sounds like your CFI needs to broaden his/her horizons a little.