As John said, the stars in and of themselves do not matter. The actual experience level of troops does.
I am unsure as to what exactly you and your friend were doing, but I will assume that you played independant games as Germany and that you took differing policy slider moves. The two typical paths are to maximize central planning or to maximize the standing army slider.
I would guess that your friend shifted the standing army slider all the way to the left, which would result in his new units starting at 20 experience points (triggering the "star" graphic). As you did not do this, your units don't get the star.
This is not a big deal. Whatever slider move choices you made, they will presumably contribute to whatever strategy you are imagining. An early shift to central planning can increase your ability to build industrially-demanding units for the early war, which may be more valuable than increased unit experience.