There's a pretty wide gap between what you think is Constitutional and what U.S. courts think.
Virginia law notwithstanding, elsewhere in the U.S., driving is not a right and never has been. Per U.S. Supreme Court law, freedom to travel includes the freedom to cross state lines, but that right does not extend to any particular mode of travel. You're free to walk, but not necessarily to drive or fly (notwithstanding 49 U.S.C. 40103, because Congress subsequently restricted that right in 49 U.S.C. 44901-44902). Otherwise, you'd just be able to walk into an airport and board any flight you'd like without presenting identification.
Similarly, if driving were a right, states would be forced to allow anyone behind a wheel (ok, at the helm of a 2-ton killdozer) without being properly trained or insured first.
I'm sure the attorneys at Ring have already been through this discussion to decide whether similar actions were warranted, and concluded otherwise.
Also, a big difference between COPS and the instant case is that in the TV shows, law enforcement have already identified the suspect, while here, the suspect is at large. I think it would be difficult to convince a court that you were the intentional target of defamation when the defendant hasn't identified you yet.
If others similarly situated could prevail on similar theories, TV shows like "COPS" and the like wouldn't be possible. The fact that they've been successfully running for over 20 years suggests that this is not the case.
Second, there's no "false light" if the recording shows the plaintiff plainly performing a criminal act.
Finally, a disclaimer of innocence until proven guilty would likely tend to negate such a defamation claim.
What's the practical difference between a TV show like "COPS" (or any of its various descendants), which features police recordings of its interactions in public with possibly-innocent suspects, and what's happening here? Is it merely the association with a commercial product?
It would be a very unusual circumstance for a person caught on camera performing a criminal act to incriminate him/herself by admitting guilt for the purpose of prevailing on a right-to-publicity action.
Moreover, every case involving right to publicity/right of likeness thus far has had a "famous" person as the plaintiff, where there's a sort of "brand goodwill" in the person's likeness and that goodwill is being misappropriated specifically to recommend or endorse a product. That's not the case here, for sure.
As an attorney (this is not legal advice), I would like to know what law might be violated by publishing these videos. They're owned by the person who recorded the video; and presumably they gave Ring a license to use them for such purposes.
The subject of the video, as far as I can tell, has no rights that might be recognized in law. There's no privacy right, as there's no reasonable expectation of privacy under such circumstances. There's no right of publicity being violated AFAICT, as there's no "brand goodwill" in the person's likeness to misappropriate.