Unless the man is a massive idiot in regards to his personal finances - which is unlikely, since he is probably quite a bit smarter than any of us, and knows a fair bit about money - I would imagine that he chose to use himself as an anecdote of how ridiculous certain requirements to refinance are. Perhaps he couldn't refi using existing assets as proof, perhaps he wanted to only use his income but the bank wouldn't accept 1099 income, perhaps something else. It's a curated example, which will of course be politicized and mocked, but that's what happens when you have anything to do with the government today (especially a part of the government so poorly understood, especially if you're a public face, especially if you're in charge of things, especially if your decisions affect many people, especially if you were in charge of the fed during a big downturn).
Just take it at face value: he wanted to use himself as an anecdote of how ridiculous some requirements are at at least one bank. That's it.
This thread is just another example of people here acting smugly superior about things they don't understand. We desire for our disliked public officials above everything else to show themselves to be hypocrites, so we may cast stones at their glass houses and feel better about our own. Fuck off.