Any team that calls itself an Agile team that doesn’t actually follow the processes properly is doing it wrong and will fail.

I mean, this statement is also weird, to imply that not following Agile implies failure. I'd say it's quite possible for a team to "falsely" execute on Agile and still pull off success. However, if that story is prominent and successful, no one is going to make a peep about it not being "true Agile", they'll only do that when it's a failure.

But really this detail is beside the point, that people want to use 'Agile' as shorthand for good methodology, but it's the way of the world that any shorthand that is popular will get co-opted and corrupted to the point of uselessness. You end up with various "interpretations" and so the meaning is diluted.

Now at a glance, this may seem an innocuous scenario, ok, Agile doesn't "mean" anything specific in practice because of people abusing it to their objectives, but it still carries the weight of "authority". So if you have a criticism like "there's way too many stupid pointless required fields in our Jira implementation, and there's a super convoluted workflow involving too many stakeholders to walk a simple ticket to completion", then you get chastised because "our workflow is anchored in Agile, and you can easily see online that Agile makes success, so you obviously don't understand success". You can try to declare "Individuals and interactions over processes and tools", but then they'll say "oh, but the stuff on the right is valuable, and it's used to facilitate the interactions between people". Thanks to Atlassian marketing, for a lot of the corporate world if you implement it in Jira, then it is, by definition, "Agile" and your peons can shut up because you are right.

Basically, things get ruined by trying to abbreviate. You may be able to cite the Agile manifesto as something specific enough yet still short, though it's still wishy washy enough to not be able to really "win" an argument with someone when deciding how you are going to move forward.