[MrLeRoy]

I thought that in a high speed accelerator, protons flattened out like pancakes?

To an observer with respect to whom the proton is moving, yes. The shapes discussed in the article are presumably in the proton's rest frame.

Also, Doesn't Gell-Mann's liquid droplet model of the nucleus allow for some "floppiness"?

Yes. I'm not sure why these results are so surprising; as a bound state of three quarks, it stands to reason that the proton would have excited states as well as a spherical ground state. Maybe the excited states are at lower energies than previously assumed ...

[lelio]

as well as a spherical ground state
The article seems to imply that a spherical shape isn't the ground state, did I read that right?
If that's the case, does that mean that experiments where you assume that you're bouncing particles off of one another and you're expecting billard ball reactions will be to be re-examined?