Loosing attachments would be a symptom of moving only the .enl file and not the associated .DATA folder. So How are they saving it? It isn’t recommended, but it may come down to terminology. the actual statement says not to use a “flash drive”.
http://clarivate.libguides.com/ld.php?content_id=34717450 – section 7.1 (How not to share a library) after the list of cloud services.
Anyway, at the risk of promoting discord with the software provider, and developers, I have kept my library on a Network drive shared with my lab for 17+ years, with out a problem. Only one user can use it at a time in its read/write location, but anyone can use the copy in the read only location, simultaneously. (our IT guys have set up a automated copy from R/W to RO folder each night). My online endnote synced library is there for an alternative backup, just in case, when something does happen and then the developers can tell me, “We told ya so!”.