The prof is right - a long-run trade deficit is only possible if you have a long-run capital inflow of a similar amount. In order to buy imports, America must exchange dollars for foreign currency. The foreign firm then has to put these dollars somewhere. Each dollar must either be hoarded as notes, or reinvested in US dollar-denominated assets. Even if they just put it in a domestic bank, the bank must then invest it in US securities (e.g. govt bonds) to earn a return.
So basically, almost all dollars used to buy foreign goods must eventually come back to the US as investment in dollar assets, or sit around as notes under people's beds. The former is vastly more commong than the latter.
Regarding the value of the dollar, it is not the size of the trade deficit that matters, but the rate at which dollar holders are willing to exchange dollars for foreign currency.
Quite apart from the theoretical argument, practical experience shows that the trade deficit is completely useless as a predictor of currency movements. America has had a large trade deficit for several decades, yet there have been long periods of extreme dollar strength, for example in the early-mid 80s, or the late 90s. If the trade deficit is so key, as Buffett says, how come the dollar had a huge rally during this period?
The relative wealth of Buffett versus the professor is about as relevant as it would be if Buffett claimed 2+2=5 and a penniless street bum said "no it isn't, it's 4".