In fact since the events occur at a known energy (they used a tuned e+e- collider) they can also look at the "Dalitz plot" which shows the mass-squared combinations of two pions and a J/psi. That's a handy way to look for structure, and they find it.
So what would 4 quarks (actually 2 quarks and 2 anti-quarks) look like? That's hard to say for sure. From the speed with which the pion and J/psi separate we know it isn't from a loosely bound system with the pion sort of orbiting the c/c-bar pair (charm and anti-charm).
As the article above says, low energy is harder to understand than high energy. That might seem odd, but imagine wooden blocks covered in velcro. At low speeds they may stick together in ways that are hard to describe, but at high speeds they bounce off each other, and at very high speeds they shatter in ways that are easily described.
The thing is too far off the mass shell to include a b-quark, since the lightest known b-meson is much heavier than the available energy. I have to run a few numbers, but this looks interesting. People have been looking for 4-quark states for quite a while.