Over the years, I've installed my share of toe space heaters.
Just about the only limitations on them, besides having the clear space for the full depth of the heater in the cabinet plinth, relates to the area immediately in front of the heater where the heated air blows.
If the floor covering is vinyl, most heater installation instructions say to run the heater at half power, or, to verify with the vinyl manufacturer the temperature rating of the vinyl. This is where NEC 110.3 might be invoked to say "not allowed by code."
Is the home messy? There is a common sense "don't smother the electric heater with a towel, etc., that could lead another electrician to think the homeowner can't be trusted to responsibly keep the heater clear of obstructions.
Since the heater is supplemental, I can't see any heating code restriction on the installation.
I think the other electrician just didn't like, for what ever reason, the idea of a toe space heater strongly enough that he turned the job down. Blaming "the Code" was the handy excuse.