The MUST be installed correctly. End of story. 
Agreed, however if they are not installed correctly it will not affect your oil circulation. If you install the rings incorrectly you can have low compression and likely burn oil, but it will not affect your oil pump.
+1 with Lucky here. They have to be done right.
If the compression rings are not installed facing the correct way. I.e. If you have the markings faced down, instead of scraping the oil & sealing the gas, it will push the residual oil up into the combustion chamber & aid consumption. The rings have a taper on the ends depending on ring design, for the purpose of not only maintaining compression on the power stroke, but also to scrape the oil.
So the dots must face upwards.
Regarding gaps, i like to have no gaps on the thrust side of the piston (i.e. the inlet side). With the oil control rings, i like to keep the main oil mesh ring with its gap in the middle on the exhaust side centerline, with each oil control retainer gap say 45 deg off that either side.
With the compression rings, i have perhaps 150 degrees apart, again centered on the exhaust side centerline, so i dont have any gaps on the thrust side (inlet side) of the piston.
Others will disagree, and thats cool. Even the manual might say something different?? I just ran in my engine, plenty of compression, plenty of go, and no smoke. Pretty much always done it this way with success.
As for the theory of the rings spinning. How much do they spin? The reason you have dowls is really for two strokes due to the presence of the ports. In 4 strokes, there is no ports, so no reason for dowls, but do the rings really spin?