I always thought “get down” meant “get on the dance floor” for a dance number, or more generally to get in the groove of the music. I never encountered this crouching thing.
In general I’m pretty cold on the concept of “audience participation”, unless it’s initiated by the audience. I’ve been at a couple of concerts where the artist(s) directed the audience to chime in at certain well-known bits of the song, sometimes dividing the audience into two or more groups to do different bits. When they get a muted response, indicating that people are only singing because they have been asked to and because the artist will look stupid if they don’t, it’s positively cringeworthy. Honestly, if it’s a much-loved chorus and the crowd want to join in, they will do so without being told to.