No, it's an analogy that you are taking literally and it is perfectly true. An infinite iteration of chance would indeed accomplish this.
But that's just the problem. The analogy fails precisely because it must be taken literally.
"Infinite time" analogies are prima facia false, because no real, man-made object remains unchanged and functional to infinity.
The typewriters break down. The monkeys die. The paper runs out. The ink dries up.
In the real world, the 2nd law of thermodynamics trumps the "infinite time" fantasies and stops them in their tracks.
Can you honestly claim that given two objects, sent flying in opposite directions within the emptiness of space, would eventually hit each other, given engouh time? It's just false. It would never, EVER happen. Even with infinite time.
Why? Because time is not the only variable involved, when you're talking about reality. Said objects would not collide, because they would hit something else first, or they would lose their momentum.
There are many imaginary events which could never, ever occur in reality, regardless of the amount of time thrown at them. Other variables preclude them.