I have heard this is the case for Spanish as well, but I don't have personal experience in that case.
So, spelling does make sense, but it's not much of a thing like in English. We have some rules to aid the process, but at the end of the day, you need to have read a lot to know how truly write a word.
That being said, I find kind of weird the cue process described in the article. I think that in Spanish we always learn by identifying letters with sounds as there's a 1 to 1 relationship in that direction. I.e. every written word has only one possible pronunciation.
And indeed, they could - eighth grade Spanish I students had to have had an A in English the previous year, so they were all decent English readers.
I’ve found that German is mostly phonetic like that, but not quite as consistent as Spanish is.
It's nowhere close to English though. Spanish spelling is a breeze, much simpler than Russian.
Unrelated factoid: in my experience, average Russian has more chances to reproduce believable Spanish pronunciation than English.