I worked in a bank (Chase Manhattan) in 1992, when my Asylum Application was still pending. EAD and SSN weresufficient. Of course, EAD was necessary then when I wasn't an asylee yet and I had to renew it annualy, but I had the right to work.
Now this year, the bank where I got the mortgage from asked me for the GC or EAD. I printed the memos from the BCIS site (or some other immigration site) about not needing EAD if you are an asylee, and they accepted it.
Of course, we're in the post 9-11 period and things have changed a lot since then.