Well it really comes down to what you are trying to represent - moving the minute hand works well if you are only concerned with subdivisions of the hour, but if you are trying to keep track of minutes, you want to know how many minutes have passed between one point and another, so for example if I am waiting for something to cook for 45 minutes, I want to wait for the minute hand to make 3/4 of a full rotation. If the minute hand jumps a significant amount, then that no longer holds true. By moving the marks instead of the hand, you keep track of the passing of minutes naturally.
I don't personally agree that it would be a usability problem - people already use wrist watches which aren't perpetually oriented up, they naturally find the zero point and understand the position of the hands relative to it. The only difference is that the zero point for the minutes will not generally be the same as the zero point for the hours. I certainly don't buy the "it's not the UI we're used to so it is a worse UI" argument. Mechanically, incrementing the marks is much simpler - I'm not even sure how you would get jumping the minute hand forward to work normally nonetheless how you would handle things like adjustments; but for moving the marks it's just another gear, which most clocks would have anyways for incrementing days. I don't think reading the time for the brief moment when the marks are in motion (and thus you know it's precisely martian-midnight) is really any issue; the only edge case I can imagine is a back to the future type situation where you are trying to determine a specific time by looking at a stopped clock (or more likely a still photo of a clock) and can't see that it is in motion, but the confusion would go away immediately when you see the hour hand pointed at the zero position.