Doesn't seem unreasonable to me, though I'm looking at it from their point of view. THEY don't want to send money until they've seen some paperwork that would indicate where their money is going and who they might have to chase if (as they may fear) something goes wrong at your end and they want a refund.
For example, I was trying to buy a hot-tub by mail-order, and the website didn't have a company address and their was only a mobile telephone number (and the person answering was clearly at home with his baby). So I asked for some paperwork showing the company address etc BEFORE I transferred loads of money to an unknown bank account. (The details never arrived so I bought from elsewhere). I can see why YOU don't want to supply a lot of personal info to a potential renter, and hopefully Eggcup will join this thread as she has the landlord's perspective, but from a punter's point of view I'm afraid I'm with the Russians.
By the way, my local restaurant-owner in Torre Del Mar is asking his camareros to learn Russian as he has identified they represent all the new money in town. Might be worth grabbing these - they'll tell their friends and you could be full for the next few years!