In theory, any tiny reduction in infection rate can make the decisive difference when the number of new infections from each existing infection is close enough to one. In practice, this is extremely unlikely to work in the real world because in reality, this is not some universal constant that is fixed at a particular value everywhere by some physical law - it varies from place to place, from job to job, from community to community, and the ones where it's below 1 will end up representing an exponentially smaller fraction of cases compared to the ones where it's above 1 meaning that the overall average won't stay below 1 for long.

Treating R, the number of infections from each case, as though it was the same everywhere is just a way of simplifying the model, but the map is not the territory and we need to be a lot more careful about whether our simplifying assumptions change the overall behaviour of the system being modelled than we have been.