Mexico isn't ice-free today, let alone during the last glacial maximum. Costa Rica used to have glaciers during the LGM that have since disappeared.

Even tropical mountaintops have ice, news at 11.

I wasn't the one insisting that Mexico and Central America were ice-free. The glaciation blocked off many high-altitude passes like the paso de cortes. Most of the taller ranges along the American cordillera had some level of glacial activity during the LGM and that meaningfully impacted regional climates throughout the Americas.

To be fair, I think that meant it was free of ice sheets, and were mostly countering the misconception that the LGM was like a snowball Earth.