If they claim it is absolutely secure then they don't understand security at all and very likely have some very lax security practices.

Yea, this is part of my research when buying stuff anymore - do I control it or is it on their network.

I refuse to use their management - it makes no sense, especially since there are numerous remote access tools available today.

What the fuck does a WiFi Access Point need a cloud connection and an account for?

Charging you money... That's why the on prem device is more expensive. They are both worth the same to sell.