The Cave, The Vis, The Shrine, and The Code

Mistress Rebecca has a vis source, which she must process at a particular shrine in a cave. The cave is in the mountains and she does not live particularly nearby. One day, going to process the vis, she discovers Master Ibrihim has set up shop there in the cave and is examining the site; she objects and he explains that he finds this site very interesting and informative, related to his studies of antediluvian magic. He is perfectly willing to remove himself while she extracts or processes the vis, but considers completely removing himself too much.

Rebecca complains to the quaesitor, explaining that this mage is defiling the duly registered vis source site by his presence. The quaesitore provides an opinion that Ibrihim should remove himself from the registered vis site, and that he should make up any loss of vis, based on the registered value of the source.

Ibrahim responds to both magae, accepting that he should remove, and that he would pay compensation and damages, but objects to being entirely barred, saying that the site itself has no vis source (he examined it for this before realizing it was a registered vis site; no vis he could find) and he does not see why his studies of the site must be blocked. In due time, Rebecca claims no compensation; it seems his presence does not harm the site. Ibrihim accordingly sues for access.

Who is in the right?

As long as Ibrihim do not steal the registred vis and do not prevent Rebecca to go and fetch it, I do not see why he could not stay there... she even could ask him to protect the source.

Can the cave be considered a Registered Vis site, if it is somewhere else that produces the Vis?
And you have already said she doesn't live nearby, so cannot be considered her Sanctum.

Rebecca considers the site essential to producing the vis (this is Rebecca Ex Miscellanea from F&F); the source of vis is afterbirth of women she has midwived, but it is always processed at this particular shrine. It is certainly not her Sanctum.