Logic? Well, if you have a web page about dogs and you want that webpage to rank well in the search engine results pages for the query "dogs" then wouldn't the actual word "dogs" appear in your content?
The 3% rule is a common misconception. A word can appear only once or it can appear a dozen times or more, and in some cases, not at all. What is important here is to support keywords and phrases. You do this by crafting sentences using your keyword and all kind of intelligent looking variables; including altered prefixes and suffixes, pluralizing, acronyms, synonymous phrases, antonyms, etc. etc. Avoid excessive repetition of your important words. Get them in heading tags indeed but don't make it obvious that you are optimizing for it.
Natural. Construct web content naturally. Place words in tags seemlessly with the Internet visitor's experience paramount and the search engines will respond accordingly, secondarily. Don't force feed the search engine and disappoint a qualified visitor. Balance. It's all about finding a balance in your keyphrase presentation.
