I don't think it would be realistic to run the full blockchain on a phone so the kind of wallet he is thinking of would have to talk back to a version of the bitcoin client running on a computer you control. I suspect this one, like Mycelium, talks to a server hosting the blockchain.
(Though with Mycelium, at least, the transaction signing does occur on the phone so it should be safe for certain values of safe)
Yes, I checked the linked software. It seems to be a web wallet with an offline GUI.
Does the Android version of Mycelium work the same way as the PC version?
@mymenace - This is not even in the ballpark.
I was not aware of a PC version. On the Android version, it relies on a server to process the blockchain but the keys are kept entirely on the local phone.
May be because it doesn't exist.

Sorry, my bad.

My knowledge regarding the actual wallet softwares was full of gaps. I read a paper about the possible implementations which mentioned some existing wallets by their names as examples for the possible wallet types. Thus, I read about how Bitcoin "Core", Mycelium or BlockChain.info work and I knew the "Core" is way too big of a snack for current smarthones but I missed that little detail about Mycelium that it's a smartphone wallet (it not only exists for Android but it doesn't even have a desktop version at all). I thought even this kind of wallet is yet to be implemented for smartphones but it's available already. Good to know.
(This happened because I can easily afford to use the Core version at home but I can't really make use of a smartphone wallet anyway.)
@macsga
Isn't that quote goes more like: "Gold is money and nothing else."?