I'll try to keep it simple and brief.
1. No speaker has just one impedance. The number they state is more like an average and how low or high the impedance is at the time depends on too many things. The reason the average is important, though, is because that's what you can expect to need to drive the majority of the time.
2. Ohm's Law (http://en.wikipedia.org/wiki/Ohm's_law
). The voltage in this case will stay constant and the resistance will be cut in half. That means in order to supply the same amount of power, the current has to double. Therein lies the issue.
3. A 4ohm speaker draws twice the current through an amplifier than an 8ohm one does. The relation isn't exactly linear, but you can expect more-or-less twice the heat (wasted energy) as well. Now you have the first criteria: ability to properly cool components from twice the amount of heat.
4. The other issue is the electronics themselves. Many components are designed to run properly within certain voltage and amperage specs and have different amounts of tolerances when run outside of them. Basically, better quality components have higher tolerances, so there's a good bet that the flagship receiver models with very high quality components can handle 4ohm without much issue, even if designed for 8ohm. You can kind of think of it like overclocking a computer: you're running a component beyond it's designed specs, but that doesn't mean it can't handle it as long it's within tolerance and properly cooled.
5. This also brings to light the quality of sound. With double the current, you're going to have an increase in noise/distortion. This usually means that components designed to drive 4ohm speakers will have much less THD than those that are not, even if they do work. While THD is very important, it is not overly so: a concept that was learned the hard way in the 70s (I think it was the 70s) when THD was pushed so low that it started causing other problems that more adversly affected the sound. As I mentioned before, you'll want to try to audition a receiver/amp with your speakers: if you do decide to go with a mainstream unit, you'll want be sure that the THD of the mainstream amp won't be too high while driving 4ohms and cause a lot of background white-noise or hum.
Also, keep in mind that an amp is powered through a power supply; so the PS has to also be able to push double the current without failing.
If the Yamaha says it can drive 4ohm fronts, then I would probably give them a quick call to verify that the warranty is still valid if you do just that. To be honest, I'm surprised that they say it's fine.
I should also mention that due to how an amp works, at maximum volume the amp is not paying attention to power (watts), so it will try to allow you to go to twice the wattage than you could with 8ohm speakers. That means if you ever crank it up, you need to be aware you're more likely to hit clipping issues if you're not paying attention.Edited by Electrocutor - 9/13/12 at 11:10am