Deutsche Boerse AG runs the XETRA system and is a private, publicly traded company. While they are of course overseen by the financial authorities, the German stock exchanges are private institutions.
Interestingly, "public" has a different meaning in English than in German in the context of a company.
In English, a public company is a company whose shares can be freely traded by the public.
In German, a public company is a company that is owned to the government. Companies that are listed on the stock market are called "kotiert".
This could hint at a cultural difference, with the Germans more strongly identifying with the government ("if it belongs to the government, it belongs to everyone"), whereas the English speaking countries might tend to identify more strongly with the economy ("if everyone owns or at least could own some shares of it, it belongs to everyone").
But "public education" refers to state run/funded schools :)
Also in the UK the "Public Sector" is government organisations.
The "private sector" is for-profit/comercial organisations, many of which are publicly traded comapanies, which is normally shortened to simply "public companies". So you could be a public company in the private sector that provides services to a public school, which is part of the private education sector.
In Ireland, both are used. A public [owned/sector] company is a government owned company while a public [limited] company (plc) is a company who's shares can be freely traded. Just "Public company" on its own can be context dependent, as publicly owned companies are often referred to as just public companies when referring to things like public-private partnerships or privatisation.
At least public sector and public vs private in the context of privatisation are used in the UK also.
The phrase "publicly owned" in English implies government-owned (which seems like the German.) I'm not sure that the phrase "public company" is a common one. "Publicly-traded"? Yes. A company "going public"? Yes. And people would know what you meant if you said "public company" in context, but they might think you were referring to a "public utility," which may or may not be government owned.
I think he is talking about Wirecard AG scandal and that company filling for insolvency. It's a huge thing that affected millions of people world wide specially their payment card solution in UK that got blocked and many companies that rely on them got their user cards blocked