They do sounds nuts!!
If it were me I would call the "original" biller and explain the situation to them and the response you got with the collection agency they are using. What you have written here is a perfect explanation of the situation and what has caused the delay in payment, etc. You could even print this out and send it to the "original" company as well as the collection agency manager.
I would be apprehensive giving my banking info to these people as well. Very unprofessional.
Best wishes in getting this settled
Jennifer