One of the answers to another question (Why did Seraph and Sati hide?) raised the point of programs using the backdoors to avoid getting copied by Smith.
I always assumed that Smith infected all the Matrix, based on Neo's talk to the Deus Ex Machina:
The program Smith has grown beyond your control. Soon he will spread through this city, as he spread through The Matrix
Shouldn't we conclude that he really got access to all of the Matrix, including the backdoors? In that case, he would have infected even the Architect, right?
How can we know whether he did or did not?