Shlichus Causing A Siman Ra

I just noticed an interesting mishna in Berochos 5:5. The mishna says that if a shaliach tzibbur makes a mistake it is a siman ra for the tzibbur because "shlucho shel adam k'moso". Now without this last part of "shlucho shel adam k'moso" I would have said it is a siman ra for the tzibbur since the fact the chazzan made a mistake is a bad reflection on the tzibbur. But the mishna doesn't say that. Rather it says the reason is "shlucho shel adam k'moso" which implies that the siman ra goes on the tzibbur thru hilchos shalichus. How is this different than "ain shaliach l'dvar aveirah"? When you appoint a shaliach to do an aveirah we don't say that you get punished for the aveirah, but the shaliach gets punished. So over here why does the siman ra go on the tzibbur?

One possibility off the top of my head is that "ain shaliach l'dvar aveirah" is based on the idea of "divrei harav divrei hatalmid divrei mi shomin"-in other words if Reuvain tells Shimon to do an aveirah, who should Shimon listen to, HKBH (the rav) or Reuvain (the talmid). By the case of tefilla you don't have such a sevara. The tzibbur never told the chazzan to make a mistake, it was all accidental. Since the sevara of "divreri harav" doesn't apply the shelichus can kick in to cause the siman ra to fall on the tzibbur.