This is going to be an interesting way to do a first post, but I'd disagree under some conditions.
Its definately the type of experience in life and not the shear quantity of it that matters for being safe in another country.
For example, I traveled solo in China when I was 18, however it would definately not be safe for just anyone to do that, I could do it since I am Chinese and had plenty of experience from my father and grandmother from similar family trips. I'd be pretty comfortable even if I was in Taiwan or Singapore too back then.
I'm actually 22 and about to graduate (5 year program =_=) and planning on going back to that area, this time traveling around South Korea and Japan. From my experience in China and from both Korean and Japanese friends' advice, I'm not worried at all, in fact my main worry is the trip costing too much money.
Now, being only 22 I'm not sure if my perception on this is right, but personally I think people in the 18-24 range can experience another country in a much different way than those who are older if they are open minded and willing to go along with the people in the country. Just seems people around our age are more willing to help out and even travel with people from different country of the same age. I've always heard people from around my area under 21 having a blast in different countries, with travel or a semester abroad. And its mostly because of the friends they make in the country, the supervision doesn't really keep you safe, its the friends you make that keeps you safe and lets you enjoy the country in a very natural way. (Now, I will admit the area I'm from is very diverse so this may play a part in it, the city I used to live in actually has more minorities than white which are just over 1/3 the population).