Hmm, going by the way it's worded, TIME does not actually deny that they called Trump or that they would've told him he was "probably" going to be Person of the Year. Their response is in the context of the person already being chosen, in which case, "probably" is not truly a foregone conclusion.
There's no doubt Trump is a liar in his own right, but I wouldn't put it past TIME employing clever wordplay to give off an impression he was lying to defend themselves from his attack. Because love him or hate him, Trump's name sells and attracts interest on both sides of the spectrum. At a point in their history where TIME is laying off hundreds of their employees, they need Trump more than he needs them, and would be more incentivized to choose him over someone like the San Juan mayor.