There’s a bit more to it than that. Obama said the words at a joint press conference with David Cameron during the referendum campaign. You don’t think they influenced him at all? They may even have fed him the actual line about being “back of the queue”. An American is more likely to say “back of the line”.
It was also a claim Obama couldn’t possibly make with any certainty since he wouldn’t be the US president when Britain left the EU. In reality once we had left why wouldn’t the USA want to do a trade deal with its closest ally (irrespective of the administration) when it has done with Canada and Australia?