This is the best advice in my opinion.
Wep-
As you may or may not have figured out by now, there is a significant amount of distrust and animosity that exists between appraisers and what are known as AMCs (Appraisal Management Companies). AMCs are engaged by the lender to facilitate the appraisal management process. While AMCs have been part of the mortgage finance landscape for a long time, their role has significantly increased in large part to a dictum from Fannie Mae and then with regulation included in the Dodd-Frank reform bill. While mortgage lenders and banks are not required to use AMCs for their ordering process, the system makes it easier to use them than not to use them. I cannot say exactly how large their market share is of the residential appraisal ordering process, but it is something on the scale of 50-60%. In practice, the larger the lender, the more likely it is that they will use an AMC as large lenders have larger lending footprints and to off-load the appraisal management process can be a cost savings for them (along with meeting a perceived requirement by the current regulation).
Many AMCs are paid a flat fee by the lender. In your case, I believe you paid $510. That may be the typical charge by the lender for your property type. The lender, in turn, pays the AMC part or all of that fee. The AMC, then, must work off that fee to (a) engage the appraiser and (b) pay for their own internal overhead and make their profit margin.
AMCs have appraiser panels. When an AMC gets an order, it then puts out to "bid" the assignment. Appraisers bid the fee they are willing to accept for that job. While AMCs are not supposed to assign the appraisal based on fee (they are supposed to assign the appraisal primarily on competence. Fees can matter, but rather than take the low fee bid the AMC is supposed to first filter by competence; then, turn-time and fee can come into the mix). While some AMCs do this, others don't or if they do, it is somewhat ironic that the competent appraiser is always the low bid appraiser.
So, what you are walking into here is one of the biggest challenges that residential appraisers are facing: The change in the business and income models since the introduction of AMCs on a large scale. And the concerns you hear about quality of the appraisals in a lowest-fee environment are real and legitimate*.
As a consequence of this dynamic, certain AMCs are considered the low of the low, and many appraisers will not work for them regardless of the fee. You can see by the reaction to the AMC you cited, where they rank in the eyes of appraisers who do mortgage lending and work with other AMCs.
Greg B's advice (quoted above) is the best. This is your transaction and a significant financial decision with consequences for you. The battle that rages between the three players in our industry (Appraiser, Lender, and AMC) is of significant importance to us. But unless you get an incompetent appraiser*, its significance to you is secondary. Yes, the entire reason why mortgage finance transactions need appraisals is because the appraiser is supposed to be the objective, independent, and impartial expert who will form an opinion of value that is based on the data and not based on pressure or hopeful outcomes. In other words, public trust (maintaining an independent and impartial valuation process that is part of a safe and sound lending industry) is why we are licensed and why we are required for many loan transactions. So, the battle that is occurring behind the curtain can impact you as a consumer, but you should know the background as to why the AMC used by your particular lender is ringing as many alarm bells as it is.
* I have to be clear on low fee: Just because an appraiser charges a low fee doesn't mean that appraiser is incompetent, unqualified, or unprofessional. I'd hate to have you go forward and assume that any appraiser the AMC sends out to you is not qualified or will not do a competent job. But experience shows that it is very difficult to consistently complete appraisals that are compliant with all the regulations we are required to adhere to when fees drop to a very low level. Everyone can have a fire sale, but a constant fire sale is not sustainable.
And I would tell the loan officer at your lender what you heard here. If what you heard here would make a difference in how you selected your next lender (perhaps inquire more on how the appraiser is selected and paid), then tell your loan officer that as well.
Best of luck to you on your loan.