While, if they're portfolio lender and they hold the loans, then they could have their own criteria. But there should be some regulations for that, like time frame, necessary documents etc. That could be specific for different state. I'm not familiar with those parts. Sorry I cannot help.
We as a correspondent, even though we lend our money out directly, we will sell the loan to Fannie Mae or Fredie Mae eventually. Usually when a refi signed closing documents, we as a bank will fund(finish) the loan unless lost job, etc big event. At least all my loans closed.
If they hold loans, usually they would have banking function like provide savings/checkings/cds etc accounts to get money to lend to out.
They could have several channels, like holding loans, correspondent and broker, and switch between channels internal to get best results, Like when one loan cannot work out switch to others to refuse a loan. You never know.
You said they cashed your check for the closing cost, that should be around 3000? Did they refund you money back?
As a background info, since late early Nov, rate went up a lot. 4.125% becomes impossible, then rate up another level since early December.