I've never heard anyone use the phrase "under the table" unless there was money being exchanged for services without going through the proper channels. Your understanding was spot on. This was a bad use of a very old phrase.
This seems like a bit of a stretch. Just because you haven't heard a term used in different contexts doesn't mean it's invalid. On review of the same text I may have rephrased it, but while imperfect, it's still understandable in the context.