I don’t believe it hangs on Mueller’s “integrity” as much as an offer of a pardon.
Do you really think it is a proper investigatory process to use someone who is guilty of major crimes, and therefore in need of a pardon, to lead investigations of anything, much less things they were previously involved in?
Of course not, if you're not sure. You charge them, then get them to spill their guts for some leniency. Mueller is not some irreplaceable super cop that some seem intent on making him out to be. Best case, he has a conflict of interest per his relationship with Comey, direct involvement with suspicious investigations of Russia in the past, etc, and should be fired from the position by someone in the DoJ.