What you propose [without seeing] sounds like it would be fine, the wire nut connections just need to be in an approved enclosure, and even the unsheathed Romex would be okay too if kept reasonably short - but it was the audacity to not use a box connector or even a simple grommet made out of the Romex sheath. 

Also, as an FYI, the 'Authority Having Jurisdiction ' [AHJ] which can be at both the county and/or the city level, can supersede the NEC with stricter codes.

As an example, I was a licensed journeyman in a large city where it was within code to run Romex straight to the furnace, there was also a neighboring suburb that only allowed EMT, and the flex your builders' contractor tried to use would have failed even if it wasn't 3" too short.

If you had a code enforcement inspection and what you pictured was approved, then either your builder is big enough to get rubber-stamped, or he kept the inspector in a continuous conversation about one of the inspector's favorite hobbies.