Forget ITA Matrix, since ITA only shows GDS prices, more and more airlines have filed NDC fares now which are cheaper than EDIFACT GDS, so you won't find them on ITA. Some OTAs have already NDC content available, and if you book directly with the airline, then of course its the same price as NDC content.

But to come back to your question:
Unless you find an OTA that can show you the full fare rules, which most of the time include the basefare on top of it, and in 99% the time the first letter of the base fare is the booking class, you won't know which class you're getting.

I'd recommend then to start booking through an actual travel agent, then you get the best of both worlds, lowest prices (+service fee) and full service.
When looking for one make sure you ask them if they already have access to all NDC fares with all airlines that support NDC already.