It is not actually "well known". The story comes from a classic must-read article from Ken Thompson. Though it was implemented at that time as a demonstration, it would be challenging to do it on a larger scale.
The main problem here is about software updates. For the malicious binary chunk to be reinjected in the compiler, should the compiler be recompiled with itself, that code must know where, precisely, it should hook itself. And this may change between versions of the compiler. When a GCC developer makes some changes in the source code, he may unwillingly break the hooking mechanism of the hypothetical replicating virus, and he would not know it. But future changes by developers cannot be predicted, let alone be accounted for in a virus which must then work in an autonomous manner.
Or, said otherwise, succeeding at writing a piece of (malicious) code which resists more than 20 years of updates and overhauling of a software as complex as GCC, would be a remarkable engineering feat, and I doubt mankind as a whole knows enough about computers to achieve that. Yet.
In the old Thompson situation, the C compiler software was not changed, only recompiled, and that made the whole thing easy (a fun and philosophically challenging eye-opener, but still technically easy).