I am not sure if this will solve your problem, but I had a similar problem.
It is my understanding that with the current version of Collector, you are unable to take Esri's Vector Tile Basemaps offline (this will change soonish I gather). So currently you will need to author your web maps with the older Raster Tile Basemaps.
However, if your organisational account manager has opted to enable "Use Esri vector basemaps in supported ArcGIS apps" in your organisational account settings, then you wont able to add the older raster-based basemaps to your maps as only the newer vector tile maps are provided by default in the basemap switcher for your AGOL account and maps. This means you cant take them offline when you open these maps in Collector.
Your administrator should unselect the above option and then you need to open your maps, add in a new basemap, save, then you should be able to take the maps offline.
But all of this still requires that you follow Dan Moore's advice on configuring the maps in AGOL for offline use.