Sounds like another one of these TRE folks who believe that the three little initials give them god like knowledge and ability. TRI's and TRE's are supposed to be teaching (and testing) manufacturer's recommended procedures, not their unfounded opinions.
As an aside, that wing tank pump doesn't keep the engine running; the high pressure pumps do that. Tank pumps ensure that a VOLUME of fuel is available to feed those high pressure pumps. Where that volume of fuel comes from (on side or off-side tank) makes no difference what-so-ever to the engine pumps. In fact, gravity does the same thing (with limitations).
Bottom line, follow the recommended procedures and question everything a TRE (or anyone else) tells you which is NOT backed up by the manufactures approved documentation.