In theory, any type of home loan could be assumable. However, only two types of typical loans have this feature: FHA loans, insured by the Federal Housing Administration, and VA loans, guaranteed by the U.S. Department of Veterans Affairs. Conventional loans typically are not assumable.
Assuming an existing mortgage can be simpler, easier and less costly for the buyer than applying for a new mortgage.
Appraisers are very careful now as they are being blamed for a lot of our mortgage crisis when prices were considered inflated to make it work. There are some terrific appraisers out there and unfortunately, they are left to clean up the mess, which makes them more conservative. Some of the basic things appraisers look for in determining a property's value are square footage, age of the home, school district, condition (i.e. newer siding, windows, re-modeled items, carpet, paint, etc.), date of the sale (lenders prefer them to be within six months) and location. Each of these has a weighted value to the appraiser (i.e. new siding on a 30 year old home is considered more of a maintenance item than an upgrade) and some items will contribute to the overall value - but not necessarily add value on their own (i.e. a kitchen remodel adds some value but won't automatically adjust your price by the amount you spent on it).
Underwriting guidelines with lenders are also much stricter. Wells Fargo may not have even been allowed to consider another appraisal due to new government guidelines.
Bottom line - don't sweat the old appraisal. There is no written record of these that another appraiser can look up - unless you happen to pull the same appraiser! Appraisers are now assigned by random drawing through a third party system to eliminate fraud and misuse. If you do happen to get the same appraiser, you will know when the appraiser calls to set up a showing. You can refuse to let that appraiser have access and they lender would have no choice but to re-assign the appraisal. That would be a last resort, but you do have the right to restrict access on your own home. The only other way someone would know about the first appraisal is if the appraiser had mentioned it to another appraiser and they talked, or your original buyer had mentioned it to someone. The original lender, Wells Fargo, would not be able to release it to anyone else without the permission of the original buyer as the original buyer would have been responsible for the cost of that appraisal.
Sound complicated enough yet??!? Don't worry - you should be fine - good luck with your sale!