I know the paper and I think that it is a cut above average but I prefer ( as you might expect) my own analysis in Stats in Medicine that he cites ( the “revisited” paper). There are two mistakes he makes in my opinion.
1) He is too easy on the Chambless and Roebuck work. Correcting for measurement error in baselines is obviously wrong for randomised studies as my two letters in SiM commenting on C&R showed.
2) Like many an epidemiologist he makes the standard implicit assumption that conditional on covariate adjustment what you have is a sort of (potentially biased) parallel group study. However it is clear that the correct analogy for his two Dutch cities example is a cluster randomised trial with, unfortunately, only two clusters.

IMO, understanding these two points leads to the following. ANCOVA is valid on the assumption that the between groups regression is equal to the within group regression. This is obviously reasonable for randomised parallel group trials and less obviously so for cut-off designs. For epidemiological studies it is obvious that it might not be true.
However, the change score analysis is wrong under any circumstance. It simultaneously requires belief that the within group covariance is incorrect for adjusting for baseline differences but that the within group variance is the right one to use for comparing means at outcome.
The change score analysis is usually justified by smuggling in a hidden tracking assumption. It is assumed that in the absence of any causal effect differences at outcome will equal differences at baseline. IMO Liang and Zeger do this in their paper on the subject.

My general opinion about this field is that it is a prime example of my maxim that understanding frequently has to precede and guide modeling rather than vice versa. I shall tweet that, I think.