While the photo was taken by her assistant, the fact is that it was Franklin's expertise in X-ray crystallography that resulted in a superior level of image quality. Her contribution is deservedly significant because if she had not used such techniques to precisely control the humidity of the imaging chamber, the images Gosling took would not have had the resolution they did.
Nope. The technique was invented by Gosling back when he was working for Wilkins, before Franklin arrived at King's College. And, yes, in doing that work he learned that humidity was the key.
Not to downplay Franklin's role-- she was doing the hard work of interpretation of the x-ray diffraction patterns-- but Photo 51 was taken by Gosling.
To say that it was Gosling's photo, thus implying that he--of anyone at Kings College--should have received some measure of credit for the discovery,
Correct: he should have received some measure of credit. And, to be fair, he did: the Nature paper (in the same issue as Watson and Crick's) was authored by Franklin and Gosling.
But Watson, Crick, and Wilkins got a Nobel prize. Gosling, who did the actual work, finished his degree, couldn't find a job in Britain, and left the field. If there's a person who was unfairly erased from the histories, it's Raymond Goslling.
is a misrepresentation in the sense that a lab assistant whose responsibility is to operate machinery is not necessarily the one who devised the method or protocol of operation,
Maybe not. That was the excuse for why Jocelyn Bell didn't share the Nobel prize for discovering pulsars. But in this case Gosling was the one who devised the method and protocol, and did so before Franklin arrived at King's college.
There's several good books on the details (although I advise you to skip Watson's book the Double Helix, which is sensational but glosses over the contributions of everybody else.)