If it were me, I'd have all the bio media and mechanical in the Eheim and remove the Fluval. Less chance of a wet floor or the noise of a freight train in your living room then...
The owner is talking bull I'm afraid. One filter you never shut down in the biological one. If you leave an external biological filter off for too long you kill all your filter bacteria and then your stuffed. Chemical medias are a waste of time and money if you maintain your tank correctly also. You have to stop chemical filtration in any tank when you add treatment, as the chemical media will remove the medications. Finally, you are un-likely to have Nitrate issues with an external filter set-up as it would have to be really clogged with rubbish to create such an issue. At that point, virtually all flow would have been lost though, and high Ammonia/Nitrite in the tank would be more concerning...
All the best
Rabbut