Open accounts are 'lines of credit." Lines of credit are similar to checking accounts, but if the owner draws more than the balance the overage becomes a short-term LOAN. This is a business practice. The banks were not financing the Watchtower.
I haven't had time to drag it out yet, but the original Russell letter is in Zion's Watch Tower for 1895. It wasn't to Rothschild, though it referenced him. It was about Jewish settlement in Palestine. Russell was a Zionist; he believed as his Literalist predecessors did that the Jews would be resettled in a reconstituted Israel. Rothschild was financing resettlement of European Jews in Palestine. Hence, Russell's interest.
Just writing to someone does not mean they support you. I've written many letters to people I would not associate with socially simply for information or to express my opinion. The "rule of thumb" behind my history writing is: "If it seems improbable, it probably is." Confirm before you believe.
I've just gotten out of the hospital, and I'm more than a little sick. Be patient, and as I can I will copy out the original letter and post it.