You are probably correct...
The second bullet point of the Mounted Combatant feat reads (PHB, p. 168):
You can force an attack targeted at your mount to target you instead.
This does not provide any qualifications such as "...if it can reach you." or "...if the attacker can see you," etc. The feat says you may redirect the attack, full stop.
Mechanically, this makes sense. Imagine a humanoid mounted on a dragon or something so large that the humanoid would never be within reach from a melee attack from any direction but directly above. Such a mount would mean the second bullet point of the Mounted Combatant feat would almost never be usable.
I think it's important to point out that the rider has the agency to redirect the attack. It is not a case like the spell sanctuary where the attacking creature has to save against some sort of an effect. Nor does it work like the Cavalier fighter's Unwavering Mark or the Ancestral Guardian barbarian's Ancestral Protectors features, where the attacker is incentivized (but not mandated) to choose a specific target.
The text doesn't provide any sort of narrative description to help describe how this feature manifests but what it seems to be attempting to simulate is the rider's ability to shift her position in the saddle to place a part of her body in the way of the incoming blow. I say "shift" because no movement is spent as a part of this feature.
...But the DM is allowed to be more correct
However, at the core of D&D 5th edition is what is colloquially called "Rule Zero", which grants the DM the power and responsibility to be the final arbiter at the table. It's found in the intro to the DMG (p. 4), under "The Dungeon Master":
The D&D rules help you and the other players have a good time, but the rules aren't in charge. You're the DM, and you are in charge of the game.
And also touched upon in the intro to the PHB (p. 6) and basic rules, under "How to Play":
- The players describe what they want to do.
- The DM narrates the results of the adventurers' actions.
I can imagine a situation where a person is riding a colossal mount. Something the size of a three-story building. The rule for the Mounted Combatant feat allows the rider to redirect an attack targeted at her mount to the rider instead. How could a rider three stories up possibly interpose her body against an attack being made down at the ground level?
The letter of the rule departs from reasonable imagination completely in this situation.
So the answer is best summed up as: the rider can redirect an attack to herself even if doing so would cause that attack to extend beyond its normal reach/range unless the DM decides that this is not feasible. In this case, what the DM says happens is what happens.