It is just the way it is said in France - il est quinze heures quinze. It may be for phonetic or elegance reasons as per the description in the lesson, or could also reflect the fact that 24 hour time is used exclusively ('military time') in many areas where precision and lack of any ambiguity is required with time  signalling - expressing the precise minutes and only expressing them as time after the hour gives much less risk of misinterpretation in those fields.

Quinze heures is military style and quart is colloquial. Never the twain shall meet.