Absolutely no. What he described is also how Ledger works and if you consider Ledger an offline wallet you are being crazy. Just because you can use it in some offline mode that doesn't make it an offline wallet. It needs an internet connection to update the firmware and the apps regularly. Most of the apps that it has can not be used without internet connection. Also, Ledger Recover anyone? A wallet that requires an internet connection to update it to continue using it can never be offline. Is ledger fully open source? I don't think so.
I never even mentioned a Ledger wallet. I did own one, but I dont use that shitty piece of hardware ever again. But what you said is
not true for the vast majority of hardware wallets. I dont know where you got the idea that I was talking about Ledger devices? I suggest you research a little more about how hardware wallets work.
We must be careful with the logic that we use, otherwise we could consider mobile wallets as offline wallets as long as we keep them then disconnected from the internet. Lol
Thats literally the definition of the word "offline". In technical contexts, it means disconnected from the network, in this case the Internet. So yes, if you have a wallet installed on a device that is disconnected from the network, that is by definition an "offline wallet." Im not arguing here that this always makes it a good option for cold storage. It depends on the setup.