Is there something special about evidential statements that justifies changing their probabilities without having updated on something else?

Linguistically, "evidence" is derived from Latin "videre" which means 'to see'. The archetypal form of getting evidence is seeing something with your own eyes.

You change your probability of E, because you see E. Why do you believe that you see E? Your visual neurons were changed in response to the signals from your retina, which is an involuntary process.