No one should consider this as evidence, one way or the other. However, for whatever it's worth ...

I've been involved in Roman re-enactment units, in the past. The scutum is carred with the palm facing up, because the thing weighs about 27 pounds. A palm-facing down carry would put tremendous strain on the hand and lower arm. Besides which, when a "barbarian" crashes a 12-pound longsword onto your shield, it's coming out of your hand, if the palm is down.

Because of the unique shape of the pilum, "clips" really aren't needed. Once the pilum is slipped between scutum and strap, it comes to a stop at a logical point. Gravity does the rest, as Ironwall correctly theorised. I also wish to point out that the scutum and two pila is a large load for the one hand and arm, especially over a long march.