The whole problem of this paper is that it just made an assumption that generating truly random numbers is trivial. It is not, it was showed many times in practice that many random number generators are poor. And if you take randomness out of this scheme, this is just another function, maybe more complex than existing ones, but that's all about it.
It should be noted that the construction of Eagle's algorithm only relies on uncertainty, not the quality of random numbers. As long as you take any number in the possible value space, using any random number generator will not affect the conclusion.
The quality of the random number generator is concerned with the quality of the random number sequence, which we don’t care about.