If anyone talking to anybody in private front of a group of people is a potentially salacious event, the level of paranoia and tension in that place is out of control. At one point, all of my direct reports were women -- if they felt anxious to have a private conversation with me in my office or stairwell, that's a huge problem, and I couldn't have been effective at my job.
So, if it's not the official policy in an office, it is probably still grounds for action, since most offices expect a certain level of ethical behavior toward coworkers.
There are reasons why managers can't generally have relationships with a direct report. HR at my company forbids it.
That being said, perhaps this is a way to work around the normal pitfalls, where if there is a potential conflict, the person in question can be a "practical" manager, but perhaps not a "supervisory" manager. Those are horrible words for it, but I mean in that one manager would be actively overseeing the work, and the other would be a lower level of involvement check/balance against the former. It may be more manpower to do this, but it's generally how the engineering teams here work out anyway; that there are the engineers who have been here longer overseeing the new hires in the work, with a more uninvolved formal supervisory structure as well.
(This has other problems, I'll openly add, but has allowed for a situation like mine to exist, so it does make me look twice.)
Sorry for the essay, this ended up being a lot longer than I had originally intended.
Also certain organizations forbid higher ranking and lower ranking people to even hang out outside of work, develop close personal relationships, or even have about personal/non-work conversations. Many militaries operate this way. My sister also worked for an organization that had this policy.
I would point out that moving in this direction is moving in a sort-of opposite direction to the direction that society went when we human made the transition to a modern capitalist/bureaucratic society. The reason you have bureaucracy, human resource, job descriptions and all the rest is that this allows a person to be separated from a job. There's lots of inveigling against "being a cog in a machine" but it should be remembered that a cog has clear obligations and clear rewards. And the cog is essentially a compartment - a person's social life, relationship involvement, cultural values and whatnot are kept at arms length. And it is a bit clunky, bureaucracy implies people aren't using these factors as means to make quicker decisions.
So in a sense, "chucking all the bureaucracy" sort of guarantees that you will have a situation where a monoculture of something will dominate. Because someone similar to the existing group can most easily "fit right in". And the aim is quick, unmediated action rather than any formal processes. (Edit: and the easiest monoculture is young white men but that would just be an example, not a PC inveigling again this particular group).
In the bureaucratic paradigm, a chat with a boss shouldn't involve implication of friendship and from there relationship interest - and in a well-function bureaucracy, it doesn't. In a start-up, the implications of a chat are totally informal and thus the implication of friend would be there and so the implication of relationship interest can easily appear - the bad part of "no walls" is clearest.