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Yes, don't do it.
You're both probably right. BUT the Paladin mount description is open-ended, permissive and inclusive of exotic mounts.
This mount is usually a heavy horse (for a Medium paladin) or a pony (for a Small paladin), although more exotic mounts, such as a boar, camel, or dog are also suitable.
The phrase "such as" is the point of flexibility.
If a Cavalier's Horse Mount stacks with a Paladin Horse Mount it would be silly for a a Cavalier (Beast Rider's) Exotic Mount not to stack with a Paladin's Mount - especially because the Core Rulebook's description of the Paladin mount is open-ended and allows for exotic mounts.
That isn't a special case; it's the standard case. The GM is responsible for deciding what mounts are available for paladins and for cavaliers.
If your question is "what mounts does PFS allow for each class", you should ask PFS, not the Pathfinder rules forum.