In the description above, ability should have been written as inability. The summary has it correct.

Does it still happen if the 'Convert XHTML to Comcode' option is on? (Admin Zone > Setup > Configuration > Site options).

Lol, ironic, I meant if the option is OFF.

We have the same problem today, must be that solar flair. I'll check into it. As of now, the only linking an image will do is to itself, as a slightly larger one (as opposed to the thumbnail).

That option is ON (checked).
On a side but related note, the image re-sizer does not function.
You have nicely fixed the 'inline' publishing functionality. (smiley face here)
I will 'OFF' it and retry.

That did it, and (as you probably would have guessed) it also fixed the image re-sizer! I take it this should be the permanent setting? Why would that (a display option) have such an effect?

It isn't in 7.1, it will be in 8. It's the way we are heading.

On that note, some comments and questions.
I have noticed some issues I previously reported as being resolved (in later installs), as I have done some scratch start-overs in my trials. Obviously the 'core' is being edited, probably on a daily basis (and also probably by Yourself). In order to keep up-to-date, and until there is another numbered upgrade, should we go to your Github and install what is available there? Or, should the 'upgrader' be used instead? I found it to be a bit daunting and had some issues, but I did not have time to work through them and provide notifications.
When is the projected v8 due out?

Could not reproduce on latest v8 code, even with Comcode conversion. Possibly due to it being fixed already (various Comcode changes have happened).