A local bank with real people in their REO office are definitely approachable. In fact, if you establish a track record of easy to deal with, word is your bond, fast, good pay, etc., etc. they may come to you with their REOs.
Every local bank with whom I have a relationship shares their REO list with me and actually emails me when they have new properties they think will peak my interest.
Large banks - forgettaboutit.
PS - I bought 3 REOs (at separate times over the period of a year or so) from a local bank that is about 5 years old with 6 or so branches. I dealt directly with the President and have come to know him personally. To the point where we have provided each other advice on general business topics. On the third purchase he gave me an offer I couldn't refuse - he agreed to match the exact terms of my normal financial institution on the loan AND knock $2k off the final negotiated price iff I finance with his bank. I took the deal. In a uncharacteristic set of circumstances (for the way I run my business) I since sold that property (I am usually a buy and hold REI) to someone who gave me an offer I couldn't refuse.