I'm not sure why the concept of the Jeans mass was dismissed originally in the OP, it seems to me that this is pretty fundamental if you want to form pretty much anything beyond grains of dust in the ISM. The point there is, you have a very low density medium (even a giant molecular cloud is pretty low density), so you can't get enough collisions to form anything larger than a few micron dust grains. The problem is that if you have GMC gas sitting inside lower density gas (the rest of the ISM), the force balance there is perfectly stable and nothing more really happens. But if you build up the Jeans mass of material in the GMC, now you have a force balance that is starting to look like gravity balancing internal pressure, and that type of balance under the nearly isothermal conditions in a GMC (enforced by the rapid exchange of heat via optically thin light propagation) is quite unstable! Thus you tend to get loss of force balance and free fall, and that is the start of forming much larger things.
The problem for forming planets, instead of stars, is that the Jeans mass is many thousands of solar masses, so you can only build smaller things (even normal stars) via fragmentation. So that leads to what gets called "the initial mass function", which kind of peaks around a solar mass. I don't know if this initial mass function is well understood yet, so it might not be so clear how the fragmentation continues down to very small scales like ice giants or even rocky (exo)planets. (The IAU dropped the ball on that one, nobody is going to be saddled with calling these exoplanets.) But I think the point above is well taken that if you start to build up too much of a rocky or icy planet, you will start pulling in hydrogen also, if there is no star nearby to either blow the hydrogen gas away or heat it up until it can't be captured. So when the Wiki talks about lone planets forming on their own, I suspect they must mean gas giants, which are basically unglorified brown dwarfs. That would just be the tail of the initial mass function, which probably does not extend down to Earthlike planets, but who's to say it's completely impossible?