Both historically had private hospital systems, and just so happen to implement pension/employer-based insurance programs very early on. German's just evolved in one direction and the US evolved in the other.
And no, we didn't had a historically significant share of private hospital systems, those came with the introduction of the DRG System, which forced many city/church owned hospitals into privatisation.
Before that, they had a "Fixed Price per Night" System, which also was a bit stupid, before that they got reimbursed their cost.