The manual for the Honda EU2000 clearly states this, but you need to be sure you adjust that little circular knob on the Fuel Cap to the operating position or the generator will certainly quit after a few minutes operation.
Our problems occurred during the ARRL Field Day 2008 and were the result of tired operators stumbling around in the darkness dealing with the generators. We were quite safe with the refueling process, but always managed to forget that fuel cap switch.
Oh well, you learn something everyday.
I will note the Honda EU2000 generator is one of the finest small generators ever built and well worth the money. There are very quiet, provide more than enough power for multiple stations and run for quite a while on a tank of gas. Another measurable benefit is the inverter approach to generating power. The very clean and frequency stable 60 Hz waveform these units provide was compatible with the UPS units we used to power our logging server computers and wireless router.
Be sure to shop around for a good price. You should be able to find this for under $800 shipped to your door. My local Honda dealer wants about $1,100 for the EU2000; I do very much like supporting local businesses with purchases like this, but my charity only goes so far.