But even though I've got 2003 on my computer, I can open docx files. There's a patch, service pack, or add on (or whatever they're called with word) that upgrades older versions of word so they can open docx. I'm sure an agent can obtain these if I did. So if they're requesting only doc or rtf files, it's because that's what they prefer.
Most agents I've researched so far seem to want initial submissions pasted in the body of an email or use online forms anyway, so I'm assuming the e-mailed word files would be for when they actually request partials or fulls.
Anyway, I'm not going to refuse to send queries (or respond to requests for partials or fulls) from agents who interest me (and you'd better believe I'm researching everyone I submit to), and who have a good reputation and track record in the industry, simply because they specify that they want rtf or doc files instead of docx.
And if I did so, it sounds like I'd be narrowing my choices pretty badly. Maybe once I'm a published writer with some bestsellers under my belt I'll be able to be that picky. Though if I end up being a bestselling author, it would suggest that my agent was doing pretty well for me, docx or no.
This has gotten pretty far off track. The OP question was about accidentally sending DOCX instead of DOC, and whether the recipient would likely be able to open it. I expressed surprise at the idea that they would not be able to. It was all downhill from there.