It's not a contradiction. It was simply a case of you not reading the documentation closely enough, or not understanding it.
DAY_OF_YEAR (along with HOUR, MINUTE, etc.) is an int constant. In the case of DAY_OF_YEAR, the value is 6. It's always 6. When you call the get(int) method, the int tells it which field you want to get. So when you say get(DAY_OF_YEAR), you're saying get(field number 6).