It would seem to be odd for a mark owner to sue after specifically putting out a favicon, which is intended to be used to visually ID that site in a sea of tabs/links.
Regardless of where the logo is acquired from what is more important is where it is shown and what it is shown next to. This is what I mean by brand sensitivity. The article makes it seem (to me) like the reviewer has a problem with a specific aspect of the app but is using a somewhat broadly interpretable part of the guidelines as the reason for rejection. This is why I suspect that a visual change regarding the logos might help the app pass review.