It might help to work an example.

Suppose we are interested in an event B with prior probability P(B) = 1/2 which is prior log odds L(B) = 0, and have observed evidence E which is worth 1 bit, so L(B|E) = 1 and P(B|E) = 2/3 ~= .67. But if we are meta uncertain of the strength of evidence E such that we assign probability 1/2 that it is worth 0 bits, and probability 1/2 that it is worth 2 bits, then the expected log odds is EL(B|E) = 1, but the expected probability EP(B|E) = (1/2)*(1/2) + (1/2)*(4/5) = (.5 + .8)/2 = .65, decreasing towards 1/2 from P(B|E) ~= .67.

But what if instead the prior probability was P(B) = 1/5, or L(B) = -2. Then, with the same evidence with the same meta uncertainty, EL(B|E) = L(B|E) = -1, P(B|E) = 1/3 ~= .33, and EP(B|E) = .35, this time increasing towards 1/2.

Note this did not even require meta uncertainty over the prior, only the uncertainty over the total posterior log-odds is important. Also note that even though uncertainty moves the expected probability towards 1/2, it does not move the expected log-odds towards 0.