Things might be stricter now, but back when I dabbled in real estate, the appraisal was a farce. The appraiser, the real estate agents, and the loan appraiser could always magically make the numbers work.
Well it's based on comps which is the last 3 houses to sell within your neighborhood. After 2008 things also got stricter. You can also "check" the appraisal by asking your insurance company for the rebuild value of your house. That may have limited utility though but if you have new development of similar sized houses in your area then the rebuild should be close to that and that will set a max prices anyway. Since why buy the old house when you can buy new. Again it's a limited argument but it's another data point.
I believe there are some new regulations that have taken the appraiser out of the back pocket of the bank. I'm not sure if it has made any difference though.