What do you mean never giving up sovereignty? The US absolutely gave up a lot of Sovereignty alongside Canada and Mexico when it signed NAFTA.
It gave up some Sovereignty when it organized NATO. It doesn't matter what the Citizens think, the fact of the matter is if a NATO member were to be caught up in a hot conflict, Americans everywhere could decry fighting over in Europe, but the US would still deploy.
Same thing in East Asia with Mutual Defense Treaties with AUS, SK and JP. Signing those required the US to give up some sovereignty in the utility of its armed forces.
There's also institutions that the US, UK and others lent their hands to creating such as the UN, IMF, World Bank so on and so forth that added a lot of baggage into what even their creators could do bureaucratically. They actually just had a session discussing this a bit
https://www.youtube.com/watch?v=cgLWQ3WkOjEStarts at about 59 minutes in an goes on till around 1:09
Finally it should be noted that he isn't really telling the UK to stay in. He offered an Opinion on why they should stay and gave his reasons, the same way other world leaders try to offer their "advice" to US voters on not pushing for Trump
Ultimately though, throughout that entire session he probably emphasises it 3 or 4 times that the Choice belongs to the British people alone since it is their country and he is offering his opinion because the workings of the UK are important to the US, and British influence as a whole is better for the EU.
You already have Visa free travel for example, but aren't forced to open borders because you have Shengen exemption.
You are part of the single market, yet do not have to tie yourself heavily to the euro necessarily in favor of Pounds.
The UK overall is a very special state in the whole of the EU with a ton of exemptions to it already, but whatever choice its people make should be respected.