Earlier quoted context omitted.
No, most “communist” countries (and I use the term loosely because really they were just state capitalist) owned many different companies, rather than being part of one mega government corporation.
Its all a spectrum but I think in practice the above statement is meaningful. In the USSR the government set ranges of wages that different firms/administrators could give out. I guess in practice you had some choice but not if you had one entity with practically unlimited negotiating power.
First of all, there were some collectively owned enterprises (cooperatives), which were a tiny bit more independent than directly state owned business. They could deviate a little from the strict, centrally directed price and wage norms etc.
Second, even in the state owned sector, there was some diversity among political attitudes. Some directors were more pragmatic and would be willing to employ even people whose cadre record was tainted (e.g. a relative defected to the West). Some directors were hardcore Communists who would never tolerate suspicious or politically unreliable characters in their workforce.
Finding a job if you were deemed politically unreliable was a big deal, because being jobless for a certain period of time was a crime punishable by prison. (Parasitism.)