I wonder if an authorised remote user (ie an affiliated researcher) can easily instruct ArchiveBox to store a URL and later retrieve it
Once you download the data and persist it on local storage, it's available to whomever has access to that drive or server.
Also, ideally a random user should be able to retrieve the archived web page or file (eg a PDF, CSV etc).
For rando access, you could put the data on a public ftp server, or even get fancier with html styled pages. If I understand you correctly, you want a random user to be reading your report that has citations, so that when a rando user clicks the citation, they are presented with whatever you downloaded with ArchiveBox. Kind of Wikipedia style. Speaking of which, a wiki framework might be just the ticket you are looking for.
Download the data, integrate it in to a selfhosted wiki, and it would be available to rando users. Of course your wiki server will have to have all the accoutrements of security so you don't get hacked by a bazillion bots.