You're being overly literal.

I have seen SIAI affiliated people on Less Wrong arguing that self modification is impossible to prevent by pointing out that even if you include an injunction against rewriting its own source-code would not prevent it from building something else.

Self modification as you describe it is a useless mathematical concept for Friendliness, as is engineering. Worse, it is not even well-defined, if an AI copies itself onto another computer, and alters the copy, is that self-modification? If it modifies itself, but keeps a copy of its old code around, is that self-modification? Where do you draw the line between the two?

You are violating the principle of charity by assuming that interpretation that makes them look worse.

Mostly when SIAI people talk about self-modification they imagine a machine that just goes in and edits its own source code because that is presumably the most efficient way to self modify and the one that most AI's would use. This does not mean the 'builds another AI' is not included, but it seems like a very stupid and inefficient way to go about things, so you are wasting your time by worrying too much about it.

I'll bet you £100 that whatever conclusions the SIAI eventually draws about self modification will apply just as well to all kinds, I really cannot see how a silly distinction like the one you are making would find its way into a mathematical proof.