Well, as stated before, I cannot explain the reason why this occurs. But when I raised the issue of not being able to see certain ads which should have been showing with my Google AdWords manager, he explained that it was a display issue as I had not shown interest on multiple searches, and gave me the Ad Preview link I posted earlier in the topic.

It is perfectly possible he was lying to me, I suppose, or that he had incorrectly diagnosed the issue. But the fact remains that my ads sometimes don't show at all, or show at much lower positions, when I search for them on normal Google than on the Ad Preview screen.

Unfortunately I haven't had a chance to test definitively whether the Ad Preview tool results are correct, but the stats from AdWords which show the average position of certain keywords seem to correlate with them, rather than with what I see when I search.