No, this is not necessarily true - what you're describing is more akin to a co-op, not an employee owned company.
An employee owned company just means there is an ESOP (Employee Stock Ownership Plan). So employees own some or all of the company's stock. That's it, it's an ownership structure, not a management structure. It says absolutely nothing about day-to-day operations or how decisions are made. The vast majority of employee owned companies are still run like a dictatorship.
Source: I've worked for multiple employees owned companies. Both were effectively dictatorships. Literally zero voting whatsoever.