The Bangkok Bank and Ayudhya Bank certainly have this policy and state that it is government policy (the dreaded 'regulation'). Don't know about the other ones but if you know of an example, please do let me know, I am getting fed up of using the overseas ones.
Two current colleagues have them. One is with TMB and the other (the rather disappointing) Amex credit card. Both are teachers.
I applied when the Mrs was preggers and turned down due to Siam Commercial Bank's policy - I needed to earn substantially more than I was to meet their requirements.
Standard Chartered Bank (I worked there quite a lot at one stage and had hypothetical discussions with staff ranging from tellers to branch mangers) definitely issue credit cards to foreigners, although I believe they have a minimum salary requirement.
I have discussed this many times in passing and seen it discussed umpteen times on forums. I have never ever heard of any bank requesting that a deposit is made to be borrowed against - this would be ridiculous and pointless, I find it hard to believe quite frankly! Although it definitely sounds like something a Thai bank teller might come out with if they weren't sure of the correct procedures!
The people I have met with credit cards are often disbelieving that others find it a problem and those who have had problems are disbelieving of those with cards IME - this seems to imply that the rules are often unclear and more likely open to interpretation on any given day.
A credit card doesn't really interest me to be honest, I had nothing but dramas with them back home. The majority of people I hear discussing the "unfairness" of Thailand and how they can't get credit cards here have never called or visited a bank to inquire about a credit card. It doesn't take a genius to work out that the transient nature of the foreign teaching profession makes us a poor credit risk as a group and that's how banks operate generally - if the risk falls outside their accepted levels they turn you down.
Compare a guy I know very well who works for a large Singaporean company in Phuket. He earns well in excess of 200k Bt and walked into a bank one afternoon and left an hour later with a credit card with a half million limit! Clearly they didn't consider him a risk!
Most guys I have met who have wanted credit cards have needed them due to their inability to manage their personal finances, exactly the type of people who would borrow 100k from a bank and disappear back home or on to a different country without giving it a thought - the same people who moan about the unfairness of Thai regulations. As far as I know there isn't a law that says "foreigners can't have Thai credit cards" - all banks make the rules for themselves, here just as anywhere else in the world.
I might feel like I would be a good credit risk if I was married with family here, had had a WP for 3 or 4 consecutive years and had a few quid stashed away in the bank. If I was in that situation I am pretty confident I could get a credit card here just as anywhere else!
I did try and telephone Bangkok Bank a moment ago to ask a few questions - but I was on hold for ages and I'm off to play golf soon and have a few things to do first!