I think you're underestimating the number of people who make $350k, or they make less but have career windfalls of much higher income. Some examples from some friends:
1. Worked for a startup, got stock options, options popped when the company got bought by a public company. They don't make $350k but they got a couple hundred grand in stock in one recent year.
2. Software Sales - had a big year, made a couple hundred thousand more than usual, used that for a down payment
3. Tech Company RSU appreciation - most tech companies give you stock pegged at a certain price when you join. If you're lucky...the stock goes up, and you get the appreciation in addition to the stock grant. I've gotten lucky on grants that got me an extra $100k here or there. Couple of my friends are in this group
4. Overtime - some nurses and cops can make crazy money if they work a lot. Not a bad way to grind for a couple years to get that chunk for the down payment, then coast a bit once you have a house.