Does Joffrey's immunity to triggered events extend to effects like that of Rusted Sword?

I would venture "Yes", but am not too sure.

If not, is there a simple way to determine the answer?

Thanks in advance for any answers.

That version of Joffrey is immune to triggered effects (not just events). However, maybe I'm not understanding your question as it relates to rusted sword. Rusted sword is an attachment and Joff is allowed to have attachments. His immunity has nothing to do with putting attachments on him.

Immunity only ignores direct effects and "choose"-type targeting.

Rusted Sword's effect works directly on itself, putting it into play and on a character. It does not "choose" or target that character. So there is nothing on Joff's immunity that stops him from having an attachment put on him with an effect like that - just like there is nothing in his immunity that stops (most) attachment removal from taking an attachment off of him.