Is 拝見いたしました an example of 二重敬語?

Question

二重敬語 is presumably considered bad style (or simply incorrect).

I hear/read 拝見いたしました all the time. Is it an example of 二重敬語?

I understood 二重敬語 to be a little more complex than "used a polite form more than once in a phrase".

To be a bit more precise, I think that to express a verb in 敬語, one should make the verb polite, but only once, so that

お読みになる

is 敬語, but

お読みになられる

is 二重敬語.

拝見いたす might be fine, because 拝見 is a (敬語) noun and いたす is a (敬語) verb; or it might be a problem, because 拝見する is a (敬語) form of 見る.

Answer 1

To answer the title question as a simple yes-no question, the only logical answer would be "Yes, it is." The phrase clearly uses a [敬語]{けいご} twice,「[拝見]{はいけん}」 and 「いたす」, which satisfies the definition of [二重敬語]{にじゅうけいご}.

Is the phrase 「拝見いたしました」 "incorrect" then? According to me, no, it is not. Why not? Because it is in such wide use and it just sounds normal and natural if you have a native ear. It carries none of the "wordiness" (and if I may, "funniness") of some of the other examples of 二重敬語 such as 「お[分]{わ}かりになられる」 and 「お[召]{め}し[上]{あ}がりになられる」.