I think OP is making two separate but related points, a general point and a specific point. Both involve guessing something that the error-handling code, on the spot, might not know.

1. When I personally see database timeouts at work it's rarely the database's fault, 99 times out of 100 it's the caller's fault for their crappy query; they should have looked at the query plan before deploying it. How is the error-handling code supposed to know? I log timeouts (that still fail after retry) as errors so someone looks at it and we get a stack trace leading me to the bad query. The database itself tracks timeout metrics but the log is much more immediately useful: it takes me straight to the scene of the crime. I think this is OP's primary point: in some cases, investigation is required to determine whether it's your service's fault or not, and the error-handling code doesn't have the information to know that.

2. As with exceptions vs. return values in code, the low-level code often doesn't know how the higher-level caller will classify a particular error. A low-level error may or may not be a high-level error; the low-level code can't know that, but the low-level code is the one doing the logging. The low-level logging might even be a third party library. This is particularly tricky when code reuse enters the picture: the same error might be "page the on-call immediately" level for one consumer, but "ignore, this is expected" for another consumer.

I think the more general point (that you should avoid logging errors for things that aren't your service's fault) stands. It's just tricky in some cases.