There's nothing to stop the author of an compiler subverting its binaries such
that *generally* infects all binaries it touches, such that those binaries then
infect all other binaries they touch (e.g. by hooking open), and this infection
could also introduce system-binary specific attacks as/when it detected it
was running as part of those programmes.
Thinking in terms of a compiler specifically looking for login is ignoring the huge
advances made in virus design since Thompson wrote his.
I.e. in this discussion we're assuming DDC means you need to subvert 2
compilers. However that's not the case, nor is it even supported by the
thesis being discussed.