If that case is so different, than the case with two marbles is also different - because removing the second-to-last marble will change will change the bag to be in that situation. But then, the case with three marbles is also different, and by induction you are left with only special cases.
On the other hand, see the related statement "If all marbles in a bag are black, adding a red marble will result in a mixed bag" clearly fails for the empty bag.
This isn't really a question of logic or mathematics. Mathematicians just use systems which are useful. And predicate logic, which has proven invaluable, would allow OP's claim.
