Trinity, It is my humble opinion that no appraiser should do an "Exterior Only" appraisal when access to the home is available. That said, it sounds as though you would have no problem granting access to your home for an appraisal given your concerns.
When you are borrowing money, you will ultimately pay for the appraisal, one way or another, whether it be through fees, points or your rate. Insist to your lender that you have an appraisal that shows true Market Value of your home, and that Market Value should include an interior inspection. If your lender refuses then find another lender. They are just trying to save some money -- typically $50-$100. I personally cite fees that the exterior appraisal report and the interior appraisal report are the same fee, because I have a hard rule (with certain exceptions) that I do not do exterior only reports.
There are some appraisers who will advocate for an "Exterior Only" inspection and cite that true Market Value can be derived. It is my humble opinion that if you are ultimately going to pay for an appraisal it should include an interior inspection of your home, you are entitled to that. You also have the right to a copy of that appraisal (Exterior or interior report) under Federal Law.
Your initial question was how accurate are Exterior (Drive-by) appraisals. Most on this forum would agree that they have a 20% accuracy problem. Make your lender do the right thing, and please keep researching for your own good. You will get good advice and bad advice.....some bad advice might come from certain Appraiser Trainees who think they know more than they do.
Good luck.
TE
Certified General in Iowa and Michigan