Typically, no you're not monitored and recorded. However, depending on your lack of trust you could always use LFS and inspect the source of everything you compile. Granted that's a laborious undertaking and not really realistic for an individual. If you think simply compiling it from source is trustworthy enough you can go with LFS or any other
source based Linux distros. Only with source based distros can you really guarantee that you hold the source code to the binaries that are running on your system.
Other than that, it's up to you to put your trust in the distribution you're using.