Private Zoom chats are public

Zoom has become extremely popular last times, due to its many features and pretty good quality:

However, in a past couple of weeks it has been affected by bad press, in respect of its privacy and security settings. Let's just bring up here Zoom's false claims about its end-to-end encryption (which was not really end-to-end..), or the problem of uninvated people turining up for meetings (so called zoom-bombing).

So, are my private Zoom messages really public?

The last security breach comes public after the claim that private chats (the chats between two persons in a meeting) are publicly visible for everybody after the meeting finishes. It turns up that all the messages, including the private ones, can be exported automatically to a file after the online call has ended.

Apparently, Zoom officially confirmed these observations:
"If a host chooses to record a Zoom meeting locally, then chats sent publicly, as well as any private chat exchanges that the host who chose to record the meeting participated in during session, are saved."

You have been warned.