I think I have an answer for this question, but I am not a scientist, so I wanted to post my ideas for critique.

Here's the premise:

http://phys.org/news/2012-08-sun-perfectly-baffles-scientists.html

Synopsis: Scientists had predicted that the Sun would have significantly more equatorial bulge than it does, and were surprised to find it is a nearly perfect sphere. If the Sun was the size of a beach ball, the equatorial bulge would be about the thickness of a human hair.

Here's my simple, straightforward hypothesis to explain: Fusion is what makes the Sun round. While Jupiter and Saturn are compositionally similar to the Sun (mosty hydrogen and helium) and exhibit prominent equatorial bulging, they do not have fusion occuring in their cores. Fusion applies pressure from the center of the Sun outward, and this tends to push the poles out, cancelling most of that flattening. Otherwise, the Sun would have a more pronounced equatorial bulge like Saturn and Jupiter.

So, I chalk up the Sun's spherical shape to hydrostatic equilibrium. According to the Internet:

"In continuum mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity at each point is constant over time. This occurs when external forces such as gravity are balanced by a pressure gradient force."

I think the same thing applies to plasma in the Sun, which behaves like a fluid in this case.

Again, I am not a scientist. I am a layman. Comments welcome.