I'm not misleading you. See Shapiro's paper. He says this: "Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path".I am a little concerned that I might be being misled, in some subtle way by Farsight. Is the explanation ref variable light speed correct in explaining the Shapiro effect. I follow the argument and it seems plausible.
That's what Einstein said too, time and time again. However after he died Peter Bergmann popularized the idea that the speed of light doesn't change with gravitational potential. See Wikipedia:
"Peter Bergmann did not agree with Einstein, but left the dispute out of his earlier book in 1942 to get Einstein’s endorsement. After Einstein died Bergmann wrote a new book in 1968 claiming that vector light velocity could change direction but not speed. This has become a prevailing opinion in science, but not in agreement with Einstein’s unambiguous math. Bergman did acknowledge that the apparent speed of light would change in a gravity field and go to zero at an event horizon as viewed by a distant observer".
It would. Note that if space expands between the galaxies but not within as per the raisin-cake analogy, every galaxy will be surrounded by a region of space where the speed of light varies. And a gravitational field is a place where the speed of light varies.If the speed of light in the vacuum is not constant away from gravitational sources ie in an expanding space, possibly expanding at different rates, then does this not make the measurements look a little more difficult.