"1. I propose that this concept be called "unex..."

I propose that this concept be called "unexpected surprise" rather than "strictly confused":

"Strictly confused" suggests logical incoherence.
"Unexpected surprise" can be motivated the following way: let $s(d) = \textrm{surprise}(d \mid H) = - \log \Pr (d \mid H)$ be how surprising data $d$ is on hypothesis $H$ . Then one is "strictly confused" if the observed $s$ is larger than than one would expect assuming a $H$ holds.

This terminology is nice because the average of $s$ under $H$ is the entropy or expected surprise in $(d \mid H)$ . It also connects with Bayes, since $\textrm{log-likelihood} = -\textrm{surprise}$ is the evidential support $d$ gives $H$ .

The section on "Distinction from frequentist p-values" is, I think, both technically incorrect and a bit uncharitable.
- It's technically incorrect because the following isn't true:
  
  The classical frequentist test for rejecting the null hypothesis involves considering the probability assigned to particular 'obvious'-seeming partitions of the data, and asking if we ended up inside a low-probability partition.
  
  Actually, the classical frequentist test involves specifying an obvious-seeming measure of surprise $t(d)$ , and seeing whether $t$ is higher than expected on $H$ . This is even more arbitrary than the above.
- On the other hand, it's uncharitable because it's widely acknowledged one should try to choose $t$ to be sufficient, which is exactly the condition that the partition induced by $t$ is "compatible" with $\Pr(d \mid H)$ for different $H$ , in the sense that $\Pr(H \mid d) = \Pr(H \mid t(d))$ for all the considered $H$ .
  
  Clearly $s$ is sufficient in this sense. But there might be simpler functions of $d$ that do the job too ("minimal sufficient statistics").
  
  Note that $t$ being sufficient doesn't make it non-arbitrary, as it may not be a monotone function of $s$ .
Finally, I think that this concept is clearly "extra-Bayesian", in the sense that it's about non-probabilistic ("Knightian") uncertainty over $H$ , and one is considering probabilities attached to unobserved $d$ (i.e., not conditioning on the observed $d$ ).

I don't think being "extra-Bayesian" in this sense is problematic. But I think it should be owned-up to.

Actually, "unexpected surprise" reveals a nice connection between Bayesian and sampling-based uncertainty intervals:
- To get a (HPD) credible interval, exclude those $H$ that are relatively surprised by the observed $d$ (or which are a priori surprising).
- To get a (nice) confidence interval, exclude those $H$ that are "unexpectedly surprised" by $d$ .