Adams doesn't need to imply it when medical SOP implies it.
I understand why Biden would not want to share that info and think that he made the right call for the situation he was in at the time (even before you consider domestic politics it's generally unwise for heads of state to talk about medical problems unless they're imminently stepping down because of them) but every man in this country over 40 knows that this cancer is screened for and someone getting "head of state" level care doesn't just get surprised by this kind of cancer at this stage unless many people were negligent.