Wood farther up? I like that one! :-)
Try not to take things too personal. We once had a series of pics here of church wiring, done by volunteers. The discussion that followed revealed that many of us had encountered unacceptable wiring in these situations.
The most common theme was the use of residential methods in a location (the church) that required commercial practices. In Reno, that means "No Romex, no plastic pipe," etc. This is but one of the reasons the mention of "Church work" make many of us shudder- and start looking for the exits!
To answer your question, equipment must be intended for its' environment, and must be used according to its' listing. "Cut in" boxes, even the metal ones, are not listed as floor boxes. Nor are the covers listed for being stepped upon. With the boxes attached to the sub-floor, you are probably also going to have flammable material (the floor) exposed to the contents of the box. It's likely the carpenters didn't even know a real box existed for this use.
Unless these are in a protected location (say, under a table), they just won't do.
