That thought, that "the number of trials doesn’t change the probability of individual trials in this case because each trial is statistically independent" is based on a false assumption that the mathematical statement, observed alone, is all we know about the issue.
And it isn't. We know that the infection happens when enough active viruses appear on the mucosa cells of the host. We know that there are a lot of viruses in every droplet from somebody's nose or mouth. Imagine how much viruses somebody leaves on the surface if he wipes his nose with a hand, for example, and then uses that hand to handle some item.
Finally, we know how much time it takes for half of the viruses to become non functioning (half life) -- something like three days, it is, they remain in the similar numbers for quite a while on the surface. Multiple touches of the same surface on which there is certain number of viruses is nothing like a series of "independent trials."
