When does consulate require census records?

[RussoTiesi]

(I apologize if this question has been answered already, but I couldn't come up with any results when using this site's search engine).

I've read various posts about people having to submit census records to the consulate. Are census records required only if the applicant submits letters of no record concerning an ancestor's naturalization?

Also, when census records are required, which years do they ask for? The 1920 and 1930 censuses clearly show that my family was in Argentina for a little while, which leads me to believe I shouldn't "forget" to mention this part of my family history.

Finally, how do they deal with discrepancies in the records themselves? In my particular case, I've been searching without success for the 1910 Chicago census of my GGF Leonardo Russo Tiesi and his wife, Anna Terranella. Last night, I found them at the address I'd expect to find them at (1157 Milton), except they are indexed as "Nardi and Marino Nurrzo." The Nardi must be a nickname for Leonardo, and perhaps Marino is a corruption of Marianna, and the handwriting for Nurrzo could also be read as Russio. All the other details, though, including years of birth and immigration, as well as the presence of Anna's two younger siblings, are spot on. Just to cover all my bases, should I begin compiling the various supporting evidence that these are indeed my ancestors' census records?

As always, I appreciate the generous help offered by participants on this board.

[johnnyonthespot]

If you have letters of no record for naturalization, the consulates ask you to provide additional proof wherever possible. One such proof is a certified copy of a census taken after the birth of (I presume) your grandfather and which shows your great-grandfather still listed as either "Al" (Alien) or "Pa" (Papers filed).

If you have naturalization documents, then the census is not required.

[amaglioc]

I never found my grandparents' marriage cert, I used uncertified, regular photocopies of census forms from ancestry.com as a way to support other documents (death certs, birth certs for father) showing they were indeed married. I don't know how seriously the photocopied census forms were taken (nobody asked for them), but Dr. Ansaldo in Houston DID look at them briefly, and I think that they contributed to an overall sense that I'd done my homework.

I should add of course that the most important substitute for the marriage cert was a letter of no record from my grandparents' home commune and several communes in the vicinity.