Trek had a multilink suspension design that had an outboard chain line for years. The bike basically wanted to pitch the chain off the outer chainring every chance it got. They also had a modified single pivot design they deemed a 4 bar link, hence faux-bar link moniker. The idea was good. The execution was hell. I don't blame you for not liking their bike. The Session was an awesome bike though. Again we are talking common vs Enzo level bikes in comparison. The early Fuel series was a shoddy single pivot/ABP split link design they tried to patch instead of fixing multiple times.
The real-long explanation:
Another implementation of the single pivot design attaches the swingarm to the shock via additional linkages, typically creating a 4-bar linkage that in actuating ("driving") the shock to create a more progressive leverage ratio between wheel travel and shock absorber travel. This designs is referred to as linkage driven single pivot, colloquially called faux-bar. It employs a four-bar linkage but the rear axle is held in a swingarm and still describes a circular axle path. The four-bar linkage serves only to actuate the shock and has no role in governing the axle path. Manufacturers of the linkage driven single pivot often use the word "four-bar" in their marketing campaigns.
If you want to know what works and what doesn't just ask. I've ridden it all from 90-2010. Nothings new. hahahaha, seriously.
I can ride my old 99' Mountain Cycle San Andreas faster than most guys can ram their new $7k super, virtual, multi, posi, negative, dead space, inter-linked, floated, and realized suspension shitter into the back of their Porsche after I beat them up and down on a ride.
It's like Jason in his beater rides smoking everyone at the Dragon. However, I can help you find a bike that makes riding fun and doesn't cost you a ton.