No idea why anyone would rent a car there. There's shuttles and taxis, and no problems getting around. Was there 3 years ago and stayed at Empire Hotel. Definitely burned into my memory as one of the nicest places I stayed at. You can spend 2 hours in their natural lagoon and not get bored.
As for non-religious sightseeing: Take a short downtown lake boat tour, ~30 mins is plenty to get an idea, also of water buildings. You'll need to haggle as they will try to upsell you to some half day tour of some remote water villages.
Afterwards, the memorabilia museum downtown is very well worth a visit, and you can easily spend 2 hours there. There's a sizeable model of the Sultan's Dreamliner in the lobby, so FT needs are fulfilled as well
2 hours lagoon, 1 hour boat tour, 2 hours museum and call it an excellent Saturday.
Remember there will be ZERO booze available to your friend. And since there are no bars, the only place to hang out at night are coffee shops (and not the good kind).
So bring your own, get a nice room at the Empire hotel, and enjoy a bottle of Red Wine on the huge balcony.
So, to answer the initial question: Renting a car is a bad idea, going to Brunei is not.