Personally, I will not do bank transfers with private individuals either on the net or even if I have met them a couple of times, again personally, I think it's reckless for someone to give me their bank acc't details to pay them it would make me a suspect if anything happens to their account.
As regards established traders, I would so long as they were established, >but<, with a debit card no need to worry for reasons already pointed out, no need for traders to inhibit their potential sales either, use Paypal! Apart from anything else, if people trade across the net any buyer should/would/does expect them to have the correct facilities in place so the buyer can spend & buy with peace of mind, the facilities are there for it.