> This means that everyone is guaranteed
I don't think that this usage of 'guaranteed' is strictly correct (although I understand the informal sense in which it is meant). I don't know a formal definition of "random number" that would allow me to back up what I'm about to say, but it seems to me impossible to guarantee that exactly 10% of all generated random numbers are less than 0.1. For example, it can't possibly be true if (some, but) fewer than 10 numbers are generated. (For example, consider jmmcd (https://news.ycombinator.com/item?id=9874773 )'s hypothetical classroom with 2 students.)
The best guarantee that I can imagine is some sort of "law of large numbers", which won't help in a class of, say, 30 people, 4 of whom happen to generate a small number!
EDIT: Also, I think that the use of a random-number generator should probably count as co-ordination. Consider, for example, a situation where some outside observer picks floor(10%*$classsize) of the class, and the random-number generator is replaced by this person. (Let's say he has an auxiliary random-number generator, for which he generates a number up to 0.1 for the chosen students, and a number past 0.1 for the unchosen.) This is clearly co-ordination, but it is also indistinguishable to anyone who can't peer behind the curtain; so it seems to me that your situation should count as co-ordination, too.
EDIT 2: Also also, let's ignore the fact that there are only finitely many distinguishable floating-point numbers in [0, 1] (so that, in particular, it makes a difference what we instruct the student to do who generates 0.1 exactly), and suppose that there's some clever output scheme that gives infinitely many possibilities.