Valve has said on at least a couple occasions they don't really have interest in making games anymore, unless there is some new technology they get interested in that they can make a game around.
The HL2 episodes were basically tests for different source engine technologies.
Alyx was basically then playing around with VR.
So yeah, I can totally see some weird fucked up thing like a brainchip being what HL3 is built around, if HL3 ever stops being anything more than a syphilitic hallucination of a desperate mind.
All their games are tests for different technologies or business models. In hindsight, Gabe has never cared about the story of Half-Life. He just happened to have hired a good writer for HL1 and HL2 by accident. It's why I'm more interested in the fanon then the canon at this point. Half-Life: Echoes and Entropy: Zero are criminally underplayed.
To be fair we know that a HL Sequel was worked on by Valve several times but always scrapped in various stages of production.
So the rumours really came from somewhere reasonable and not just from pure speculation and desperation.