I've found it in a book and assume it's got to be correct, but I cannot understand why the Past Perfect of I had been offered. Would was offered not have been clearer?
I explained that when I was in high school I had been offered a job teaching tennis at a local country club because I had been one of the best junior tennis players in the area
The past perfect in this example suggests that the writer is going to talk about something that happened at a point in the past after the had beens, or that he has already done so: a "main thing" that the past perfect is supposed to provide background information to.
If there were no such "main thing" for the had beens to introduce, then the past perfect would probably be inferior to the non-perfect past. But it can be seen in the actual text that there does follow a "main thing":
The last sentence, I never enjoyed..., is the "main thing" that the had beens are the background to. Alternatively, you could say the explanation to the FBI as a whole, which happened in the past, is the "main thing". Or a combination.
When I was in highschool is not in the past perfect, because I would say it describes something that provides background to the has beens but did not happen before them; only background information that happened before a main thing in the past are normally in the past perfect (of course there are exceptions to all this).
Past perfect expresses a past within a past -- a time prior to some past time. In your example, the past tense of "explained" refers to a past time when the explaining took place, and the "when I was in high school" refers to a time even before the time of explaining. Thus, a past within a past.
This example with the past perfect isn't really specific to reported speech. You could replace "explained" by "knew" or "realized" or "recalled", and you'd still get a past perfect.
"Was offered" would also be okay in this example. I don't think it would be clearer, but it would be as clear.
