I've already found the problem. Webmail was "normal", no visible issues there.
I found the cause to be that the webmail had its normal, usual INBOX, translated to our language, "Postvak IN".
Then, when inspecting the folder structure in WebMail, I noticed (after looking multiple times, 50+ folders) that there was another item "Inbox" as a subfolder of the root Inbox.
I tried renaming that to InboxOLD and voila, suddenly SelectInbox() did work as expected.
It seems that, long before I was even working here, we have been working with Lotus Notes and that has been completely replaced by Microsoft Office (for years already).
We believe this migration process to be the culprit of this extra Inbox folder and causing errors for the users that have had their account since then. What's strange is that, up until today, we never received any errors or complaints. Maybe MS changed something.