That depends on the cloud service in question. The "big three" (AWS, Azure, GCP) certainly are not, but there are a lot of small/niche hosters running Kubernetes, OpenStack and other FOSS cloud software.
What part of that doesn't make sense? If the program is going to run on someone else's system then you'll need access to that system to be able to modify it to do your computing as you wish.
If you borrow my linux notebook for an hour and I don't give you access to chaning the software on it, doesn't change that linux is free software.
In the same way that free software distributers are not required to distribute your desired patches. They perform a service of distribution (or cloud providers: running the software)
But I think I get that you consider cloud services non-free outside of the pure software aspect. I think, though, that there's still meaningful distinction between providers running direct free software which you could essentially clone completely and run your own version and such that run closed versions, which do not allow that.
With regard to the individual software each customer uses, often small/niche hosts do allow each customer to inspect and modify the software. That's kind of the point of cloud VM hosting, that you "have root" and can even modify your kernel if you wish.
But that changes if you publish an interface to the software on your cloud machine, and allow others to use it. Now it's a "service" and that software is no longer free, because you have denied the four freedoms to its users.
Software as a service cannot be free software - it is a fundamental contradiction.