Yes, having a natural looking rhinoplasty is a possible outcome. The problem is, as I have posted before, many individuals approach their surgeon with unrealistic expectations. When they do not come out from surgery with the nose they envisioned (due to unrealistic expectations, surgeon error, insufficient research on the part of the patient, etc.), they take one of several roads. They remain unhappy with their new nose and constantly complain about it, and/or become anti-plastic surgery. They might also get trapped in the vicious cycle of repeat surgeries. Sometimes they can correct the original botched surgery, but most times they just keep getting their nose (and so many other things) worked on. A person who gets a bad nose job (or other surgery for that matter), may also resort to altering their appearance drastically, via means of body modification or masochistically ruining their visage.
You cannot go into a plastic surgeon's office with a nose that you determine requires alteration, and demand a tiny button nose/perfect nose/beautiful nose/ just like ... insert celebrity name here.
On the other hand, I know of several surgeron's that have done beautiful work. It looks reasonable (sometimes the price isn't), natural, and not like a cookie cutter nose. If you have not located a surgeon that can produce results such as this ... keep looking!