Sorry, but this isn't true (or more accurately, isn't the whole story).
Yes, the Freons are somewhat heavier, but the driving force from concentration differences will still drive "some" molecules into the stratosphere. And there are other driving forces at work. Thunderstorms are also particularly effective in forcing vertical circulation, even of heavy molecules (Freons are not very soluble in water drops).
And yes, the Freons ARE very thermally stable. But the breakdown mechanism in the stratosphere is photochemical, not thermal. UV radiation is present in the stratosphere which doesn't reach ground level, as it is blocked by the oxygen in the atmosphere.
The primary culprit in the breakdown of Freon is the Flourine. Flourine reacts with almost anything. Here is an interesting fact, volcanoes put tons of Flourine compounds into the atmosphere when they erupt. When mount Pinutabo erupted in the Philippines, it put more Fluorine compounds into the atmosphere in its first few seconds than man had ever produced. The Pinutabo eruption lasted 38 minutes if I remember correctly.
The bottom line is that our mere presence on Earth is insignificant compared to what nature produces. Consequently, what we do as humans is pretty minor.