But probability isn't the same as saying a system is random. Classical systems follow probability and this doesn't imply things happen randomly. As for the 'it's entirely random' claim, clearly it isn't. One such method of decay of a system is by associating the rate of decay with its motion. This is far from saying there is no physical parameters which are not directly affecting the decay rate. This type of radiation which will lead to a decay if it can, is called Larmor radiation. And changing the decay rate of a system, by altering further physical situations, further adds evidence it is a dynamical property - associated to a system, in dynamical ways.