Yes, and that's the reason why they abandoned plans to look at San Jose and are now focusing on building back in Oakland. Somewhat off topic, but the A's actually granted the Giants the territorial rights to Santa Clara County in 1990 so that the Giants could explore building a stadium in Santa Clara. A measure was put up to vote and it failed, so the Giants' owner decided shortly thereafter to move to St. Petersburg. But a local ownership group came in and bought the Giants, keeping them in the Bay Area, and then built what is now Oracle Park in 2000. When the A's asked the Giants for the rights back to Santa Clara County a few years ago, the Giants refused, MLB agreed, and that was the end of the A's dalliance with San Jose.
Bringing it back to radio, one of the owners of the Giants is KNBR radio (now owned by Cumulus), and the ownership share has survived all the corporate radio owners throughout the years. This is one of the reasons why the A's can't find a radio deal, because Cumulus also owns very good radio signals in the Bay Area, including KSFO, KGO, and KTCT (branded as "KNBR 1050"). There's no chance at all that the A's would wind up on any of those stations because of Cumulus' ownership share in the Giants, so that locks the A's out of several options.