That was it. Exactly as I was expecting, I was missing something, and you guys pointed out exactly what I did wrong.
I was selecting the cluster instead of a single host.
If I select a single host everything is OK and I can deploy it wherever I wish, on any datastore.
Thanks!
This opens another question at this point: if I wanted to deploy a VM "on the cluster" and let vSphere place wherever it wants using DRS, would I need a shared storage assigned to the cluster (as opposed to local disks attached to the hosts)? Is this correct?