We know that the aliens that are visiting are advanced, because they've crossed the stars. Therefore we know that they're engineering their vehicles using advanced technology and can find elegant solutions that aren't trivial. A key to an elegant solution is reducing it to the absolute minimum.
Given this, why do three legs work better than four? While it's been rightly noted that four legs allows the minimum three-for-stability and the fourth leg can move, humans (amongst other creatures) prove that you can balance on two legs. Indeed, you can balance on one leg, if your reflexive balancing systems are sensitive enough and strong enough. Taken to the extreme, you could balance on a pin - your reflexes and strength just has to be high enough.
Standing in place isn't the same as moving, however, which is presumably necessary. To efficiently move at a gallop, you really only need two points of contact, but it helps to have 'pushing'. When we look at a cheetah running, we see that the back feet are largely 'pushing' and the front are 'guiding'. If we posit we have the strength and reflexive balance at an advanced level, we only need one guiding foot, and can rely on the pushing feet for speed. A similar but reverse example of this is how the striders in Dark Crystal move.
But, if we assume all three feet have equal capability we get something even better than that: the ability to immediately change direction with the minimum number of limbs. If traveling in some direction, switching to a direction that is 120 degrees offset becomes trivial.
Also as noted in another post, three limbs makes climbing easy. If you've been rock climbing you have seen people using a deadpoint technique that utilizes dynamic momentum to bring their hands within reach of a good hold. These sorts of techniques make climbing much more graceful and use less energy than static three-point holds while a fourth limb is moving. Assuming the tripod is required to climb at some point, it really only needs three limbs to execute quick climbing manuevers: one 'swing point', one 'reaching point' that is about to take a hold and one 'stable point' that is about to let go once the new hold is secured.
Finally, three limbs are useful in the water. Assuming an undulating motion, similar to octopodes, any number of limbs past two would be useful. But the difficulty with only two limbs is that some degree of stabilizer is needed to maintain orientation - a fin or a third (or more) pushing appendage. Additional limbs can cause, at the least, additional drag, while their marginal utility is unclear.
Given a three dimensional space and sufficient reflexive systems and strength technology, three limbs seems like a reasonable, minimum number when the environment you're in is potentially quite variable.