Correct (if you mean to say that all errors apparently caused by lack of updating can also be framed as being caused by wrongly holding something fixed) for a sufficiently wide sense of not fixed. The fact that you are considering to replace odd results in counterfactual worlds with even results and not the other way round, or the fact that the utility of drawing a red ball is 1 and for a blue ball -2 in my example (did you get around to taking a look at it?) both have to be considered not fixed in that sense.
Basically in the terminology of this comment you can consider anything in X1 fixed and avoid the error I'm talking about by updating. Or you can avoid that error by not holding it fixed in the first place. The same holds for anything in X2 for which the decision will never have any consequences anywhere it's not true (or at least all its implications fully carry over), though that's obviously more dangerous (and has the side effect of splitting the agent into different versions in different environments).
The error you're talking about (the very error which UDT is correction for) is holding something in X2 fixed and updating when it does have outside consequences. Sometimes the error will only manifest when you actually update and only holding fixed gives results equivalent to the correct ones.
The test to see whether it's allowable to update on x is to check whether the update results in the same answers as an updateless analysis that does not hold x fixed. If an analysis with update on x and one that holds x fixed but does not update disagree the problem is not always with the analysis with update. In fact in all problems CDT and UDT agree (most boring problems) the version with update should be correct and the version that only holds fixed might not be.
Consider the following thought experiment ("Counterfactual Calculation"):
Should you write "even" on the counterfactual test sheet, given that you're 99% sure that the answer is "even"?
This thought experiment contrasts "logical knowledge" (the usual kind) and "observational knowledge" (what you get when you look at a calculator display). The kind of knowledge you obtain by observing things is not like the kind of knowledge you obtain by thinking yourself. What is the difference (if there actually is a difference)? Why does observational knowledge work in your own possible worlds, but not in counterfactuals? How much of logical knowledge is like observational knowledge, and what are the conditions of its applicability? Can things that we consider "logical knowledge" fail to apply to some counterfactuals?
(Updateless analysis would say "observational knowledge is not knowledge" or that it's knowledge only in the sense that you should bet a certain way. This doesn't analyze the intuition of knowing the result after looking at a calculator display. There is a very salient sense in which the result becomes known, and the purpose of this thought experiment is to explore some of counterintuitive properties of such knowledge.)