Pre-approval is different than approval. What you have described does not sound like the pre-approval process. Anyone can go to an online mortgage site (e.g. Countrywide) and get "pre-approved" by submitting a simple form with a little personal information. This can take a couple of seconds or maybe a day; but it is not an "official" approval. A pre-approval just gives a ballpark idea of what you could qualify for at what rate and how much your payments would be.
When you get to the point where you have signed a sales contract and the mortgage broker is actually processing the loan, this could take a couple days to complete. They will verify everything: income, credit history, etc. before getting back to you (or they may approve the loan on some sort of contingency, e.g. an appraisal).
The fact that he told you how much your payments would be means nothing... that's a simple calculation that can be done knowing only the purchase price (or loan amount), the loan term and rate.
If you're on social security, I'm not sure how they verify this; the letter may suffice for the pre-approval, but I'm sure the lender will want to see tax records or receive verification from the IRS before approval.
Many, many closings over the past three years.