“No alias” in Rust is a simple rule that was there from the start (it didn’t break any programs, unless by “programs” you mean “programs I would like to write in a certain way”).
By "breaking programs incompatible with that model" I think he means making it impossible (or requiring a tedious amount of uses of `unsafe`) to write code in Rust to be linked with C code if the C code contains idiom fairly common in C code.
To elaborate, there is a recurring trend of sound C programs turning into unsound Rust programs, because shared mutability is often necessary but Stacked Borrows places strict conditions on constructing &mut T (they invalidate some but not all aliasing *const T), and it's less ergonomic to work solely in raw pointers and avoid creating Box<T> or long-lasting &mut T (or for intrusive collections, any &mut T at all).
