Fair points...though I also got the vibe that the Team involving Ruby and Yangs parents were not necessarily the team they had in school, and that much like many military based organisations that people are divided into units. But that is honestly conjecture with no real support in the show.  Then again the only support we have for them being the school team is that they we have only seem teams within the school. The Rwby world is very lightly fleshed out. Food for thought at least. 

And Honestly , in this fantasy world of color and fairy tail named people, that they wouldn't just keep using the same naming scheme in the school that is training them for for life as a pro-hunter. Like in Military school, which the Hunting schools basically are ( A far more light version to be sure but meh ), they use the same sort of squad naming scheme and structure that they use in the military proper. But again, there simply isn't enough information to say for sure one way or another.