Ubuntu, you are too free with your jargon, and in being so you build straw-man arguments such as "'Random system' is a contradiction in terms." You simply feel that "system" is defined to mean the same thing as "deterministic system", and it looks like nobody here agrees that that's a good definition.
As for what you feel is a lack of understanding on the part of scientists as to what goes on on small scales, it turns out that your conception of the state of scientific knowledge is just plain wrong. Scientists are fairly confident that they know how things work on fairly small scales, small enough to have plenty of room to detect probabilistic behavior and still have a theory to describe that behavior.
If a random value is produced by a system how can it be random? Let's say we generate (for convienience's sake I'll pick a number) 42. Either a) our value is produced by nothing or b) our value is produced by a system. If it has no cause it doesn't make a lot of sense, and if it is produced by a system it can't be random (unless the the system is random. Then we will have the same problem to deal with and we start back at the point of origin in our thought).
The system would have to create this value, effect, energy, matter, force, whatever it is that we are dubbing "random." If the system works along the lines of 12 + 30 there we have a source for 42.
Let's say the a fundamental particlem cube-shaped particles called Okopipi's which interact by exchanging energy through even smaller photon-like particles called Yuzi are further than present understanding.
If a trillion tiny particles called Okopipi's make up a Boneko, a trillion of which makes up a Lonhern, a trillion of which make up a Xebian, a trillion of which make up a Zonadite, a trillion of which make up a Tekton, a trillion of which make up a String, or Electron, or Quark, and we see unexpected behaviour from these subatomic particles, this would be due to the behaviour of Yuzi and Okopipi's not an unknown source of Chaos from the Realm Beyond.
By claiming something is random you will have to defend that it comes from NO SOURCE because if a random outcome is generated by a system, known or unknown, a) the system must be random (in which case we are faced with the same problem all over again) or b) it is in fact, not random, because a system produced it, and the system cannot produce random values unless it too is random, where we would need to either a) create infinite systems (turtles all the way down) - which still would not have a random source - or b) claim that there is no source at all for these random values and that they simply came from nothing.
Lack of knowledge does not equal randomness, as lack of cause for the seasons does not mean that God is responsible.