In summary, you're right and he's wrong; HA is much simpler, FT is very strict.
VMware High Availability (HA)
Restart virtual machines on other vSphere hosts in the cluster without
manual intervention when a server outage is detected.
http://www.vmware.com/uk/products/vsphere/features/high-availability
An individual virtual machine can't be set for High Availability. High Availability (HA) is something you configure at the level of a cluster, not an individual virtual machine. Because of that, HA has no particular involvement with snapshots or disk provisioning models.
VMware Fault Tolerance (FT)
continuous availability for applications in the event of server
failures by creating a live shadow instance of a virtual machine that
is always up-to-date with the primary virtual machine. In the event of
a hardware outage, vSphere FT automatically triggers failover—ensuring
zero downtime
http://www.vmware.com/uk/products/vsphere/features/fault-tolerance
Fault Tolerance Snapshots
Note: As taking snapshots of FT virtual machines is not supported
http://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=1016619
Fault Tolerance and Thin Provisioning
The shared virtual disks must be in the eagerzeroedthick disk format to facilitate clustering configurations, such as Microsoft Clustering service and VMware Fault Tolerance.
http://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=1033570
But it seems like you can enable FT on a VM with thin provisioned disks, but it will cause the disks to be changed and that will take time and disk space.
Be aware that if you turn on FT on a VM, and that VM is using a thinly provisioned VMDK, that VMDK is inflated with zeroes.
http://blogs.vmware.com/vsphere/2012/03/thin-provisioning-whats-the-scoop.html