While your observation is generally on target, I would caution you on two counts:
1) Although Japanese word order is, by any measure, more flexible than English (in part because particles serve to dictate grammatical relationships in a role similar to how word order functions in English), it is perhaps a bit of an exaggeration to say that a Japanese sentence can be in any order. Adjectives and relative clauses still need to precede the nouns they modify, particles govern the nouns that come before them rather than after, some temporal and counting expressions almost invariably appear in a certain position, etc. etc. It is good to understand the basic SOV structure and prepare for exceptions, but understand that there is some rhyme or reason to how the words in a sentence are ordered, especially in contexts where it is necessary for clarification (as you observe).
2) Be careful thinking that the verb has to be at the end of every sentence in practice. Although the general structure of Japanese is SOV, you will often find inverted or incomplete sentences, or sentences that do not contain verbs at all, but instead other predicates (adjective/copula). Again, it is good to be aware of the rules, but understand that some rules (not all) are often broken.