I think you're confused by the term "permissions". You can give more freedom to the license and a copier can remove them as long as it doesn't remove the freedom that are in AGPLv3. The OnlyOffice team claim comes from the next paragraph of section 7:

> Notwithstanding any other provision of this License, for material you add to a covered work, you may [...] supplement the terms of this License with terms:

> b) Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or

This is what they did and what the other part stripped from their blatant copy. So no, removing the logo or the OnlyOffice terms therefore seems forbidden by the license itself, revoking it for the other part, thus they are now making a counterfeit.