Not sure why you would find it necessary to fill the keg 100% full of sanitizer. I'm sure it works, I just wanted to relate a different approach.
It's the only practical way to get all the air out. The other method (what I actually use) is to run steam through for about 15 minutes. This displaces all the air and sanitizes at the same time.
For sanitizing, I just make up a half gallon of StarSan solution, take the keg apart and dunk the parts in StarSan, put it back together, dump in the StarSan, close it up and shake, then dump the StarSan back out. Has worked 100% of the time for me.
Not much to the sanitizing part. As long as you get everything wet with an effective sanitizeer you are there. Getting air out is the tricky part.
As for filling the keg with beer, filling the empty, sanitized keg with CO2 and then opening the relief valve three times or so will purge it of air.
Think about this for a minute. You have a keg at 14.7 psia (1 atmosphere) air. You pressurize to 30 psig. That's 45 psia (lets call an atmosphere 15 psia to make the math a little easier. Total pressure 45 pisa, air 15 psia for 1/3 air. Bleed that back to 15 psia. Now you have a partial pressure of air of 5 psia in there. Repressurize to 30 psig i.e. 45 psia. You now have 40 psia partial pressure of CO2 and 5 psia air i.e. 1/9. Bleed back and repeat. You now have 1/27 atmosphere air for, bled back to 0 psig (15 psia) that's 0.2 psia air or 0.04 psia partial pressure of oxygen - a lot more than you want. Looked at another way you have 19000 mL gas in the keg after three repeats. 19000/27 = 703 mL air and of that 1/5th or 140 mL is oxygen.
You can, of course, "solve" this problem by purging more times or using a higher pressure of CO2 each time or both. But you are wasting a lot of CO2 in so doing. Much easier, IMO, to displace the air with something that really displaces it.
Then you can siphon the beer into the keg with no worries--even with the lid open, the CO2 will stay in the keg since it's heavier than air. Then close it up and purge the headspace with CO2 a couple times and bring up to pressure.
I suppose this would work (including the poor purging) for beer that isn't to be kept very long and for beer where diacetyl isn't a concern. But oxygen is a bad boy - responsible for staling and diacetyl and you really want to do everything you can to combat it. Displacement of all air with water or sanitizer is a pretty easy way to be sure you have it all out. The advantages of counter pressure filling are well worth the trouble.
Using these methods I've had kegged beers stay good for over 2 years.