Of course not. Science deals in evidence for and against theories and hypotheses, not "proof". And the anomalously small (compared to other elephants) mammoth ears are only one of a coordinated suite of features consistent with cold adaptation: body size and shape, hair, tusk configuration, etc. The author of your webpage doesn't seem to understand much of the evidence. I don't know if he's right about "erector muscles" on the hairs or not, but that's irrelevant to the mammoth's configuration. The thick, soft woolly underhair traps heat simply by it's fine texture and thickness, and the coarse guard hairs on the outside of the coat keep out the wind and shed moisture.
Fluffing/erecting the hair as the author suggests would not help keep the mammoths warm, as the author suggests. Quite the opposite. It would only perturb the whole system by also disturbing the guard hair layer and opening the lower layers to the environment.
Finally, mammoths aside, the paleobotany (evidence from fossil pollen, plants in the frozen mammoths' stomaches, etc) is TOTALLY out of whack with the author's claim that the animals inhabited a "tropical" climate.