Whilst the baby was strapped in we were allowed to keep him in there - this has been on more than one flight. I admit this wasn't wild 'jump you out of your seat' type turbulence, but enough to tell people to sit down and put seat belts on.
With small children who haven't been sitting up long, the reins work well in that if you tether one side to one end of the basinet and the other to the other then it basically keeps them sitting upright safely. It also helps on long flights if you think you're ALL going to go to sleep (some hopes!) - obviously let the baby have enough slack to lie down! - that you don't have to worry that whilst you're reclining, dozing, the baby might wake up, sit up and topple out.
I used the reins purely because on one flight my little boy suddenly pushed himself up (having only done it at home about twice before) and did a head-first forward somersault into my husband's lap luckily much to the amazement of everyone in the loo for the toilets queuing past our seats. After that we always used the reins for our peace of mind and it worked well.