This is fair given what Ethereum just did. But, IMO, that's not what I expect if someone says "warrant canary". Under the "original" sense of canaries, your scenarios wouldn't make sense. Unfortunately, this new, wrong interpretation of the original idea seems to have become more common.
The original idea was that on some regular cadence (say weekly), you actively post a (hopefully signed) message somewhere saying "I hereby attest that, as of <insert current date>, we have not received any warrants/subpeonas/etc and are not subject to any gag orders, etc. etc.". (eg, rsync.net's canary: https://www.rsync.net/resources/notices/canary.txt). You have to set it up so that someone has to actually go and do something for the updated canary to go up, so it's like a dead man's switch. If you ever stop posting those, that's the signal to users that something is up.
That approach is extremely robust legally. In the US at least, publicly posting a digitally signed message asserting something presumably important and valuable about your business that's knowingly a lie would be considered false advertising, wire fraud, etc. depending on the exact situation. The government has a lot of power to legally compel you to not do things that would otherwise be legal (eg, uttering the speech "we just got a subpeona for all of your data!"). What they absolutely cannot legally do is compel you to do something illegal. Eg, they can't make you commit wire fraud by actively lying to your customers about the services you provide. That's a very strong legal position and you wouldn't have a hard time getting a lawyer to back you up on it.
Basically, if your "canary" requires you to "take down" something, it's not a proper canary and, yeah, I wouldn't trust it to protect you from much.