HSBC (not UK) will sign the document for opening accounts but will have to charge me approximately US$4 to do it. This is really sad....

Please let this thread continue.
If non-HSBC, I found out that Westpac seems a bit decent if you put A$2000 into their bank.

Just a guess (don't take this the wrong way, just correct me) do you mean HSBC India? I'm surprised they're charging to sign this document, I'd have thought they want to keep A/Cs enough to do this FOC. Did you complain to the manager? Usually works. HSBC is an excellent bank with a fine tradition, true also in India (I don't mean the old UK Midland Bank which HongKong and Shanghai Banking Corporation bought a few years ago and is taking a while to turn around, culture-wise). If you raise your complaint up a level or two, you will win. I honestly know, won't say why for privacy reasons, I just do. No way will Honkers & Shankers charge you for an internal referral.

Certainly here in the UK my branch signed the papers with no questions asked - I had forgotton to take a copy of my passport and she made the photocopy for me FOC.