Awair integration: is it really 'local polling' if it doesn't work without connecting to the internet?

I have 2 Awair Elements integrated via the local API. I deeply regret buying these because they keep having connectivity issues, but that’s a subject for another post (but seriously, buyer beware! Also horrible customer service). While experimenting with different router settings (none of which solved the problem) I discovered something weird: when I block the Awairs’ internet access (while still allowing access to the intranet) the sensor becomes unavailable in HA after a couple of minutes. Which kind of surprised me, because isn’t the whole point of the local API that you don’t rely on a cloud service or share your data with it? And if this really is the case, shouldn’t the ‘Local polling’ label be changed to ‘Cloud polling’. This could potentially mean that if the company EOLs the service or goes bankrupt (which wouldn’t surprise me at all) the devices would stop working. Can anyone corroborate my findings? Am I missing something?

Awair - Home Assistant.

That says there is a local and a cloud version.

If you have evidence that there is some discrepancy, perhaps a core issue against that integration with all your evidence might be in order.

Reporting issues - Home Assistant.

Issues · home-assistant/core · GitHub.