Yes, burnt valves can affect compression, however, either the mechanic didn't do a full diagnostic or you aren't relaying all the test results. He should have done a wet test and a CLT (cylinder leakage test) along with the compression test. These tests would have pointed to the failing components. I would not rebuild the whole engine if it isn't necessary. It's like going in for major surgery and having other things removed or worked on just because you are already opened up. I would suggest a second opinion from another shop considering the amount of cash you could be spending for no reason.

Good luck,
Peter

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