Perfect litmus test indeed! I worked in one place where scrum master - the person explicitly assigned to protect the team - was the one who most loudly imposed that the company configured Jira shall be used. Despite this being brought up as a PITA every retrospective.
This is the moment you know you are doing fake Agile and your scrummaster is just the managers puppet in disguise to spy on the team.
It is difficult for the Scrum Master to be impartial in a situation where the management ultimately decides who will be the Scrum Master and whether Scrum will be used at all.
I am not sure what would be the right solution. One possibility is to fire the management, or never even hire them at first place -- if you want to have a software company that uses Scrum, do it from start. Another possibility is to have a Scrum Master with strong political skils... which more or less means, it cannot be a former developer.
Probably the fatal mistake is having too many managers in the company. At that moment, it is practically guaranteed that they will try to interfere with everything. They have to, because that is how they protect their own jobs. And they will hire more managers, because that is one way to get higher on the company ladder (hire more people into positions below you). And at that moment, everything is doomed, because now the company serves the managers instead of the other way round.
I guess this means that Scrum can work as intended only in small companies. Where the Scrum Master is not below several layers of management, but on the same level as the few managers, right below the company owner.
This is the moment you know you are doing fake Agile and your scrummaster is just the managers puppet in disguise to spy on the team.