Not true. Tom Duff regaled us of his first UNIX virus at a USENIX breakout session in 1988. The basic infection technique is to read the executable header, identifying the starting address for the code segment, save it, add your own code to the end of the code segment, patch the start address to run your "virus" code, then patch a section of your "virus" code to run the original entry point. Your "virus" can then scan all the executables in the current directory and PATH and infect all that you can successfully write. The technique works and spreads like wildfire in an environment with NFS mounted filesystem to "share" the garbage.
You will do little or no damage to the OS without root privileges.