If you install an anti-virus program that can detect "suspicious" files and upload them to a server in country X run by company Y, and you don't disable that "feature", then it's possible that your files will be seen by company Y and its employees, the intelligence service of country X, and any random hacker that's managed to gain access to those servers. This applies whatever country X is - Russia, USA, or other.
Now, the company has a strong motive to keep that data private, and to secure its servers to stop hackers getting into them, but it can't do anything about its local intelligence service. For most people, the intelligence service won't be interested in them or their files.
However, you clearly shouldn't be installing such an anti-virus program on government computers handling information that country X wants! (Or if you must install it, then you should disable the cloud upload feature).
On a related note, if you install any program, and that program includes automatic updates, then your computer will automatically download and run "updates" from the manufacturer, or from the intelligence service of the country hosting the update servers, or from any random hacker who has hacked both the update server and the code-signing key. If you don't want to give full access to your PC to the intelligence service of that country, then you should not install their software.