It’s an easy mistake to make. The key thing is that the protons don’t care about where they are. They’re just not that smart. Classically, all they need is enough kinetic energy to get close enough to overcome the Coulomb barrier. Quantum mechanically, they don’t need quite that much energy, just enough for their proximity to be close enough that their wave functions have significant overlap (or equivalently, that their KE can “tunnel” through the Coulomb Barrier.)
And this happens at the same energy whether the impetus is gravity, lasers, or Maxwell’s Demons.