A pegasus is described thusly with regards to mounts:
[T]hese wild and shy creatures are as intelligent as humanoids, and so can’t be traditionally broken and tamed. A pegasus must be persuaded to serve a good-aligned creature as a mount, but when it does so, it forges a life-long bond with its new companion.
They have an intelligence of 10 and are "as intelligent as humanoids". Intelligent creatures cannot be used as a controlled mount. So, clearly if a normal pegasus were used as a mount they would presumably qualify as "intelligent" and thus would not act as a controlled mount.
However, find greater steed says:
You control the mount in combat.
Does this mean that the find greater steed is intended to override the general mounted combat rules and force the mount to be a controlled mount?
If so, does that then mean that you cannot allow the mount to act independently?
The latter interpretation seems to mesh with a Jeremy Crawford ruling about find steed, but I'm not sure if there is something I am missing here.