I think you are right, Anthony! In the original query, first_search (or gar with), first_search[270] is the first entry on the new date!!! (and also first_search[269] is the same entry as broken_query[269], so the search results are the same up to that point).
I will still make a simple example all can try, but I think Anthony is right -- it only checks the date, not the time! Luis.