On re-reading your question, I realize I partly misunderstood it. No way that Horse Guards would have insisted on the use of two-ranks--quite the opposite. Horse Guards kept trying to sustain the "Rules and Regulations" of 1792 and constantly reiterated that everyone was to adhere to it...and it broadly insisted on three-ranks (an insistence widely side-stepped in practice, for drill and reduced units were authorized two ranks).
Your source has it wrong, backwards, and inside out!
Cheers - Howie