Sorry your friend is dead wrong. I've been building computer systems both professionally and for myself since 1996. With the exception of some of the Cyrix chips (very old don't worry about it). The stock fans have always been enough.
Some things to consider when building your gaming rig.
1) Airflow, make sure you invest in some cable ties. It's less of a problem these days thanks to SATA connections, but you should still be sure to tie your cables away from any spinning fans, and try not to let them block the spaces between the vents on your PC case. Some cases come with a funnel, attached to the inside of the case aimed above the processor socket, these are good because it allows unrestricted air to be blown across your CPU.
2) Positioning your computer. I can't tell you how many times I've seen a user decide to shove their PC into a cabinate with no airholes! This is not a good idea!! Most users won't make this mistake, but I've seen this, or users placing it into tight spaces, or stuffy area's too often not to mention it. The funnel I mentioned to you before only works if the side of the case see's fresh air.
3) Overclocking. This is were a lot of the fan debate really springs from, overclocking your CPU for a few extra cycles may seem like a good idea. I never do it personally, for the simple reason that I value stability and longevity over speed. Over clocking despite what many users will cry, does cause your system to overheat and the system to exhibit odd behaviours. Stock fans are designed to keep your processor cool at their recommended speed. Some users will show off water cooling systems and claim other wonderful ways of keeping your system cool. But at the end of the day, if you "need" that speed, just buy a better CPU! Only overclock a system if you can afford for that system to fail. Personally, I'm not that rich!
4) Noise reduction, this is a good reason for getting a different type of CPU fan, some of the noiseless models are quite good, but if you're going for this, please bare in mind all the other bits that make noise. There's no point slapping in a 3 fan nVidia 590 graphics card into your system and then buying a slient CPU fan. Same goes for the PSU. I often find the loudest bit of the machine is the DVD/ Bluray drive, and those 3.5 inch HDD's are not quiet by any means.
So if you're going to build your system for silence, then you need to research everything that goes into it, not just the fan.
Anyway that about cover's it I think. If you don't plan to overclock, or reduce noise, then don't bother. The fans that come with CPU's are designed to work. You certainly don't need to spend $100 on a new one, if you were prepared to spend that much extra, invest in a better graphics card instead. I'm sure for $50 extra you could get a decent upgrade