In fact the opposite is true.
Open source software is protected by copyright. If it were not, then any company could co-opt it and make it their own. Depending on the license, “free software” which is a distinction frequently (and some would say tediously) insisted upon by open source leading lights like the inimitable Richard Stallman, this software may impose a restriction on the rules by which reproduction or distribution of the software may be done - including modified versions of the software.
This free software is freedom-enhanced or freedom-protecting. That's free as in speech, not free as in beer.
This free software is freedom-enhanced or freedom-protecting. That's free as in speech, not free as in beer.
The famous GPL (GNU Public License) is like this - some say it is “viral”. If you or any company makes a product which is the result of modifying open source code which is licensed under the GPL, then the modifications you have made must not be published without the same affordances, indeed not without the same exact license. Notably this requires you to provide access to the the full source code without preventing anyone from further adding or modifying it.
Copyright law enables this because without such protections, software licenses would not be necessary. Failure to follow the terms of the license make one’s distribution of software a violation of copyright. Many companies have been busted because they have not followed the licenses and these days technology companies are familiar with meeting their obligations on this matter.
You may notice that most consumer electronic devices - computers, TVs etc. contain code (e.g. Linux), the license of which requires the manufacturer to tell you that you have the right to obtain the source code and that the manufacturer cannot deny you this right - nor can you deny anyone else the same rights should you decide to take that Samsung TV firmware and make a better version! Believe it or not, people do this sort of thing. You might get a bundle of open source licenses along with your equally impenetrable operation manual.
There are other licenses which are extremely permissive, such as the MIT license or the BSD license which do not place these viral restrictions on distributions. Some people believe this is more convenient, especially for software that is ideally suited to being incorporated in proprietary products as one of many components. However, just like GPL, whatever provisions the licenses do make - if these are the only terms under which the software is provided then they stick because copyright is an exclusive right to distribute unless it is explicitly assigned.
Lastly, copyright assignment is completely independent of the terms of a license. Typically copyright is held like title deeds and not given to users of the software. Exceptions are if the work is undertaken as "work for hire" where someone pays someone else to develop that software - typically copyright is assigned in exchange for the money - and another common case of copyright assignment is when an individual developer submits a modification to be included in an official open source project. Such open source projects (like Apache) have a foundation that exists to hold the copyright so that the stewardship of the software can be maintained without a messy consultation with hundreds of dispersed pseudonymous bedroom hackers who happened to have made a small contribution.