The issue presented doesn’t seem to be “an up to date browser check” it seems to be a “is it latest chrome” check, which is a very different thing.
If the organization is indeed enabling a specific check for Chrome that seems a little over the top but they're the ones supporting their users and if they want to make their life easier by only dealing with one browser that's their decision to make. It's like saying that everyone has to use Windows, or a specific line of laptops, or any other standardization to simplify the support workload.
I don’t see why I should give affordances of good will to Google here.
They’re not stupid, they know that this is an effective lever to further cement full-fat chrome as the default browser for the internet.
Why did you even compare it to IE6, out of the curiosity?
Of course Google is going to suggest using Chrome, if they detect that the browser might be out of date.