This is truly a strange and confusing method available for the da.SearchCursor. I mean the GROUP BY clause is normally applied because you are attempting to summarize things (say SUM or AVERAGE, or other some such metric). But it is entirely weird to require ObjectID which would negate any ability to correctly perform such aggragetion, let alone not even be able to include such a thing as COUNT, MIN, MAX, AVERGE, etc...
I hope I am simply missing the obvious here.