Say 1.1.0 adds a new function, and 1.1.1 fixes a bug in an old function. I write some code which uses both functions, and would hit the bug before 1.1.1. This code has to be used with >=1.1.1, or it won't work. If it's used with something <1.1.0, it won't compile, and if it's used with 1.1.0, it will compile but not work; the distinction between those clearly isn't significant. So in practice, 1.1.0 -> 1.1.1 is as meaningful an increment as 1.0.0 -> 1.1.0.
Semver would have been better with just major and minor versions.