What is the relationship between induction of cell differentiation and DNA methylation status?
This is a good question. I'm not as steeped in this literature as I'd like, but here is my understanding of the process:

Methylation is one of the key methods by which cell fate is restricted. The review you're reading is giving specific examples of cell lines that are at least partially restricted into cells that are of an entirely different type. Thus de-methylation is a method for de-differentiation, which then allows differentiation along a different line.

Your three examples that it sounds like you're interpreting as induction of differentiation, are actually examples of that effect -- de-differentiation that then allows for differentiation to a different fate. Constantinides work, for example, showed the conversion of a non-myoblast precursor into functional striated muscle cells. Not only can fibroblasts be turned into muscle cells, myoblast cell lines can be made to look like bone cells or fat cells. None of these things would happen without re-programming the cell fate by de-differentiating the cell lines to form dis-similar differentiation products.

This is consistent with other findings about de-methylation in vivo. An important example is the global de-methylation of primordial germ cells, as demonstrated in this figure from the linked review, summarizing the methylation state of the germ line in mice. Pay particular attention to the blue line. The pronucleus of the highly differentiated spermatazoon (along with its highly methylated DNA and histones) undergoes global de-methylation. Its products include the primordial germ cells of the developing mouse, the most de-differentiated state, which, in the case that it is a male, then become methylated as they become primed to differentiate, and then differentiate.