Debian is quite an opinionated project and they take matters like these very seriously. Pages like these don't exist to judge packages, they're merely there to make people who do care aware of any risks they might not have heard of, and help them exercise control over their machine if they consider these "risks" not to be worth it.

I doubt anyone will really care about version checks, unless that's the only reason your tool needs internet access at all. Maybe if you make it an opt-out rather than an opt-in feature (or don't prompt the user at all), I'd be annoyed by that (but I know others aren't).

They're completely unnecessary in packaged Debian software because the Debian people will provide newer versions of your application for their users, so a flag to opt out would be nice. Using this data in a useful way, like adding a message like "new version available" would be confusing, because there is no new version available when you run the system update tool!

Personally I'd say it should be possible to disable version checks through build flags if you intend to package software through official repositories.

If you intend to do distribution and updates yourself I don't think you should be forced to alter your code if people decide to add your software to their distribution. The burden of removing confusion and making their version stick to their ideals should be on them. It would be nice to cooperate, but I don't think you can be blamed for someone else's redistribution.