That letter of interpretation isn't worth the paper it was printed on, by the way.
As a number of folks have already tried to explain, that interpretation does
not say you can't borrow an airplane and only pay for fuel. (I don't see the word "borrow" anywhere in the letter). And the "value" is low because the FAA Chief Counsel's office has chosen to publish its responses to questions even if the response is nothing more that, "Sorry, the answer depends on information you haven't given us":
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We cannot issue an interpretation for your particular circumstances because you have not provided enough details about the exact nature of the arrangement and the purpose and intent of the flight.
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The Chief Counsel is telling the pilot that it depends on the arrangement. That in order to be "compensation" it has to be in exchange for somehting.
1. "Take my brand new G36 Bonanza over to Big City to pick up an order for some some food and drinks for the reception I'm doing next week. On the way back, go wherever you want for a few days. Just bring it back to me with full tanks."
2. "Sure you can borrow my new G36 Bonanza for a few days. Just bring it back to me with full tanks."
In both cases, the pilot is receiving something of value (free use of a an aircraft that has a pretty high dry rental value). But in only one case is the pilot receiving "compensation" because the owner is also receiving something of value in exchange.
Don't see the difference? Could be you don't want to.