Very fallacious reasoning here. No-one is saying that infections are driven by Mexican immigrants.
Rather they’re pointing out the obvious: if you’re trying to get to zero COVID, all it takes is one person to start the chain. Thus you cannot have ANY illegal immigration.
FWIW I strongly oppose the “zero COVID” goal because it’s completely unrealistic. We’ll see if the island nations can maintain it long-term but certainly in the US it’s a non-starter.