All three have wildly different values and historically corporations aren't very good at listening to anyone that isn't waving a check. They use reasoning like "priorities" to close source formerly open source projects, bend project values to reflect their own values, and wedge projects with funding in exchange for representation or control. Corporate controlled and born projects are often used as marketing or for good PR, a cursory browsing of a company's Twitter page will show how they utilize it for this type of end.
I don't really read Mitchell's speak as corporate or double speak, but I do think that referring to HashiCorp (and other) projects as "open source" is a half truth. The line that I draw here is that I don't think Mitchell is lying, rather, I think that open source is now an umbrella term that means very little and really terms like open core, free and open source software, etc are more concise. We owe that outcome to inviting our corporate friends into the fold of open source with not enough restrictions, tracking, and accountability but there's a piece of me that feels this outcome was largely intentional because it's become a means to an end as I described above. These could just be feelings but the situation is common enough that it's relatable.
I'd encourage corporations to be more transparent in their verbiage, their investments, and their representation in these projects so that it doesn't continue to confuse people who participate in and enjoy the "free" side of open source. When I look at an open source project I'd love to know if a majority of the maintainers or funding comes from a corporation. If those things are true, then as someone who highly believes in the ideals of free software I may want to stay far away from people who are susceptible to corporate influence and values. On the other hand, that increased transparency may help clear the air and prevent issues from being perceived as non-transparent or outright misrepresentation.