We have a nidan at my dojo who first studied aikido under Frank Doran Sensei in San Fransico. This nidan always begins practice with each individual with "Onegaishimasu" at the start of each technique. His definition of it is about the same as what Sensei Clark has said above, but I've never seen any issue with it as far as rank goes.
My interpretation of it is: it's just good manners! Saying Onegaishimasu is, in my mind, asking someone to train with you in such a way as to help you learn and neither of you get hurt. And afterwards, you thank them with "Domo arigato."
My organization is AAA, and I've seen it done this way at seminars as well as in my own dojo. Dunno if this will help... hope so.