I think there's a perfectly easy way to achieve this, mechanically. Just like there's a 12-element (3x4) solution grid on each card that lets you test a location to see whether the temple is there or not, we could equally well put a second solution grid on the opposite end of the card, to check for local rumors. The key question is what form that information would take; space in the grid is tight and it would be limited to a several-letter clue at most, or more likely, an abbreviation.
This scheme would integrate well with the "climbing" approach to giving location clues. In such a scheme, the several levels of clues about the temple's location would track the progress of the artifact that rests in the temple, from its origin at some location through several additional cities (or not, keeping in mind that sometimes, the clues don't "climb" at all, and Level 1 or Level 2 knowledge is the end of the line...) If there's an additional guideline imposed that prevents the artifact from "jumping" more than two cities away between links in the chain from clue to clue, then local rumors could say simply whether the artifact passed through that particular city or not. Based on your other knowledge, you could judge where such a result points to the temple potentially being located; maybe additionally, digging in a city that does test favorably for local rumors, even if the temple isn't there, at least authorizes you to look at a clue, so you at least get something for the knowledge.
Like so many other things, this feels a bit like one thing too many, but at the same time, I like the idea of letting players assemble information in different ways and from different sources. It's probably important not to have the "temple location" category work in this same way in every scenario, lest it get stale, but it may have some potential. (Actually, the bigger concern I have is just with the physical component itself -- will a player inadvertently put the wrong end of the card into the board, thinking he's checking local rumors but in fact checking for the temple?