SpaceX have run the simulations and while Red Dragon is possible, there's no way they can adapt Dragon to land on the Moon without adding an extra stage. That difference is entirely down to Aerobraking. Even the thin atmosphere of Mars makes a huge difference.
Anyone who plays KSP can confirm this for you, especially using the Real Solar System mod, though the same lessson is apparent even in the stock game.
We can also look at delta-V charts. Earth to the Moon is like 16.4km/s, Earth to Mars is like 14.3km/s using every available aerobraking opportunity (6.4km/s saved) and assuming 500m/s for the final powered landing. (The Red Dragon plan called for aerobraking from 6km/s to 540m/s and then switching to thrusters.)
Is that 2.1km/s really a whole extra stage? Or can it be met by reducing cargo capacity somewhat?
Two interesting points about Red Dragon - it wasn't feasible to put parachutes on it so its aerobraking would have been greatly limited. It wouldn't have much surface to use for deceleration in that case. I'm curious just how long it would have spent aerobraking, SpaceX's docs don't seem to mention that. And it was cancelled a few months ago with the intent of designing a "vastly" heavier lander, for which aerobraking will be that much less practical.
edit: But I can do a back of the envelope calculation. Decelerating 6500kg from 6km/s to 540m/s is 116G joules. The diameter is 3.6 meters so a molecule of air in from of the Dragon would be displaced (on average) 0.53 meters. Let's assume the atmosphere is a constant density (0.020 kg/m^3). Assume a drag coefficient of 0.05 (and ignoring the lifting body effect) that is around 200kN of force, tapering down to 1.5kN. That is like 3000 km of aerobraking at maximum atmospheric density and should take around 2300 seconds. But that depends a lot on the deorbit profile. I'm going to need a bigger simulation...
For Red Dragon they were going to add an asymmetrical 'sled' under the capsule that alters its geometry to form a lifting body, so it could spend significantly more time up in the atmosphere braking than most custom designed landers would. The sled would be jettisoned immediately before the propulsive landing.
It's not an ideal design, but this way they would only have had to make minor changes to the capsule, mainly to add more fuel for the landing than the regular design.
Okay, I concede it is totally possible. After including Nasa's atmosphere model and some drag coefficients from super-sonic bullets, it looks like Red Dragon's aerobraking maneuver would take 1600 seconds, cover 4800km and leave them with 3600 meters of altitude. (Those supersonic drag coefs were what really made the difference since they are around 0.3 at hypersonic and rise to 0.6 as it slows.)
Anyone who plays KSP can confirm this for you, especially using the Real Solar System mod, though the same lessson is apparent even in the stock game.