Hi all,
Please find this response from ESRI, on 12/02/2016:
It looks like you are experiencing BUG-000092486
BUG-000092486 states the following:
Collector for ArcGIS (iOS) 10.3.5 returns the error, "Unable to download the map. File opened that is not a database file," when downloading an offline map from an ArcGIS 10.3.1 for Server site secured with web-tier authentication.
The only workarounds at this moment are to use Collector for ArcGIS on Android or disable web tier authentication on your server, both of which may not be desirable for you or your customer.
When I asked about timeline for fix, this was the response:
Unfortunately not [known] at this time. It has been assigned to a developer and has a high status. It could be addressed in the next version.
Hmmmm....