Generally if you approach probability as an extension of logic, probability is always relative to some evidence/

Maybe, but so what? That doesn't establish any point of interest. It doesn't establish Bayes over Frequentisim, since frequentists still need evidence. And it doesn't establish subectivity over objectivty, because if there are objective probabilities, you still need evidence to know what they are.

The invalid argument I alluded to elsewhere in this thread is the argument that if there is subjective probability, based on limited information, then there is no objective probability.

So thinking probabilities existing as "things itself" taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities.

"Don't take objective probability to an extreme" is very different to "reject objective probability".