Why are your managers attending stand up? The Daily Scrum is the team's meeting. I swear Scrum is only fragile because no one reads the bloody book, or if they do they skim it or ignore it.
From the scrum guide... "The Daily Scrum is a 15-minute time-boxed event for the Development Team."
It is the team's event, if there are other people there it should be at their request. The guide goes on to say that.. "If others are present, the Scrum Master ensures that they do not disrupt the meeting."
If something is self-organized, there is no need for all this ceremony and bullshit that comes with capital-A Agile or Scrum. You just shoot the shit and talk about what you're doing.
Stand-ups and all the process attendant appears to be universally imposed from on high as a micromanagement technique, or because they were sold the idea as some kind of silver bullet by a talk or a snake-oil consultant.
I think Scrum provides a good baseline of working for new teams, but ultimately the team is free to shape it however it works best for them.
The main value of Scrum as an official process, is that it gives you a stick with which to chase toxic management out of the room. They're not sufficiently Scrum if they crash your meetings and demand to be in charge. Though in my experience, most companies that do Scrum have a management that keeps their distance unless invited.
From the scrum guide... "The Daily Scrum is a 15-minute time-boxed event for the Development Team."
It is the team's event, if there are other people there it should be at their request. The guide goes on to say that.. "If others are present, the Scrum Master ensures that they do not disrupt the meeting."