It's actually kind of reported speech of reported speech, isn't it? As you know, we usually backshift verbs when indirectly reporting speech, but you should only backshift once.
Your example is a little odd because it's not clear when Paul's help is needed. Logic says it's in the future, and so John is saying that Paul offered to help -- but in that case it seems more idiomatic to use need. The backshift to needed is what makes it sound like a direct quote of an indirect quote. Normal conversation isn't that complicated:
John said Paul would help us if we need a volunteer.
Still, needed is fine, and would likely pass without notice.
John said Paul would help us if we needed a volunteer.
Although your reference says otherwise, there is no reason to shift from the simple past to a perfect tense. The perfect tense is normally used to establish a relationship between two events in time. Your example is just a simple statement. Changing it to the perfect only makes it more confusing.
However, the perfect tense does work if the help was needed in the past, and John is only now telling me that Paul offered help at the time.
John said that Paul would have helped us if we had needed the help. Gee, thanks John, for not saying something sooner.
