While I do agree with you on how the labels technically should be used, the whole Hispanic/Latino label is actually a bit of a debate among the various groups, and maybe depends on where you are in the states and how some specific groups feel about it, and Americans use the labels interchangeably, so it gets pretty confusing and messy, lol. ^_^;;
I've heard people in Eastern coast prefer Hispanic, while Western coast peeps prefer Latino. Not sure why that is.
I've heard Puerto Ricans being more in the Hispanic label, but they can be included in the Latino label as well, which makes it more confusing for me. XD
Some people get offended by these labels and would prefer either their national country (i.e. Puerto Rican), or be called Americans. Some don't like the "Hispanic" label because it's an American term. (Colonial term?)
Here, where I live and grew up in, I often heard either Hispanic or the specific country (Puerto Rican, Cuban, etc). My family says Hispanic or Boriqua, though they do group themselves with the Latino label if there is no other option.
As a child, I was told to put down White under Race options, so that is how I often filled those papers out. I'm very American, I guess.
It's still all a very confusing mess, and I still have identity crisises and am still learning stuff, so I could be wrong. I am merely giving my own experience and what I've been told by other Latinos/Hispanic peeps. (And they don't all agree on this stuff, so...)
I don't know what else to put down for Race on those annoying papers, since I'm not Black, Alaskan, Asian, Pacific, Hawaiian, etc. I guess Other (if there is a choice for that)? Though I don't know if that is reserved for Bi-racial/Multiracial people?
I'm American, and I associate with American stuff, and can sort of "pass" as White, so...