Where did you get the idea that "statement" in Eliezer's comment is to be understood in your idiosyncratic sense of "utterances that may or may not be 'propositions'"? Not only do I dispute this, I explicitly did so earlier when I wrote (emphasis added):

Neither the grandparent nor (so far as I can tell) the great-grandparent makes the distinction between "statements" and "propositions" that you have drawn elsewhere.

Indeed, it is manifestly clear from this sentence in his comment:

it's questionable whether you can even call that a statement, since you can't say anything about its truth-conditions.

that Eliezer means by "statement" what you have insisted on calling a "proposition": something with truth-conditions, i.e. which is capable of assuming a truth-value. I, in turn, simply followed this usage in my reply. I have never had the slightest interest in entering a sub-discussion about whether this is a good choice of terminology. Furthermore, I deny the following:

Probabilities may be assigned to [statements/propositions/what-the-heck-ever] being true even if they are...neither true nor false.

and, indeed, regard the falsity of that claim as a basic background assumption upon which my entire discussion was premised.

Perhaps it would make things clearer if the linguistic terminology ("statement", "proposition", etc) were abandoned altogether (being really inappropriate to begin with), in favor of the term "hypothesis". I can then state my position in (hopefully) unambiguous terms: all hypotheses are either true or false (otherwise they are not hypotheses), hypotheses are the only entities to which probabilities may be assigned, and a Bayesian with literally zero information about whether a hypothesis is true or false must assign it a probability of 50% -- the last point being an abstract technicality that seldom if ever needs to be mentioned explicitly, lest it cause confusion of the sort we have been seeing here (so that Bayesian Bob indeed made a mistake by saying it, although I am impressed with Zed for having him say it).

Make sense now?