This has been very easy for me as both a DIY landlord who does almost all his own work and a financial independence frugalist.

Big into personal finance and love the financial independence mindset.

My wife and I wanted to flip this house because we love real estate, we want to be financially independent, and we want to improve communities in the beautiful city of Detroit.

They should provide an appraisal, of course, but if you want to pay for your own independent appraisal they shouldn't have a problem with that.As @Jim K. mentioned, going lower-tier - esp for a new investor looking OOS - is a risky move.

Good luck building wealth and becoming financially independent!

In the spirit of the holiday I would probably offer to compensate them for it after they told me what it was worth, but if it was anything more than $50 I would make them prove the value independently before I gave them anything else, and if it was significant and my contract with the company didn't waive them of damages, I would file against the company's insurance. 

A test performed by you will likely not inspire confidence by the tenant as it is not an independent third party.Mold out of normal range levels can sometimes by some seen as not that bad and with others that have more sensitive allergies or other existing health issues the effects can be felt much greater.

I have been studying & gaining my owe knowledge by independently taking action, reading the book's (most i find are recommendations of BiggerPockets) i listen to about two bigger pockets podcast a day.

Financial independence?

Why not pay for two independent home inspections and see if the second guy finds anything the first guy missed?