By all accounts, Phil isn't a pot-stirrer and he's pretty honest and isn't a sensationalist by any means. I believe what he reported. At the same time, I do believe that the "shopping" of Jones reports is something that likely happened a while ago and it's essentially new reporting of old news, which I mentioned in the bit I wrote about it.
I think teams, before making any QB or personnel decisions prior to free agency, checked the temperature of where Belichick was at with Jones and that may have been perceived as "shopping" him if he asked, "What are you offering?" but then said, "no" if it wasn't enticing enough to even ponder.
But I feel like that door is closed at this point, with the team instead moving forward to 2023. Yet the media reports, while potentially accurate in theory, may just be way behind the timeline of when all of this may have actually occurred. Or at least that's my opinion, which doesn't mean a whole lot, but whatever.