Hola Robert

Good question!

When we use más que here the meaning/nuance is different, we are highlighting the fact that it was "only" 15 minutes, whereas if I say something like: 

La entrevista no duró más de 15 minutes.

All I'm saying here is the "limit", so it lasted 15 minutes (not 10, not 20) 

Here are another two contrasting examples: 

1. No tardaron más de 5 años en construirlo.

2. No tardaron más que 5 años en construirlo. 

Number 1 is stating the number of years they took to build it and that was no longer than 5 years.

Number 2 is expressing the surprise of this having taken "just/only" 5 years.

I hope this clarified it.

Saludos

Inma