The question must be asked "When it it best to ask for examination vs. not?"
Magicians, by our very nature (we tend to be suspicious about everything) will go out of our way to "prove" all is fair, not realizing that in so doing we actually create the opposite affect in the mind of the average layman; we create suspicion when we push too much at making things look "fair". That is why I love the theory shared in Kenton Knepper's book INDIRECTION in that it teaches us how to "prove" a point without being as deliberate as to say,
"here, take a look and make certain that there are not trap doors, mirrors or hidden compartments..."
In escape work as well as mentalism trying to make things appear to be too "genuine" can and will work against you. It's best to JUST DO IT and then AFTER THE FACT, let people look to their heart's content. There is one prop I will take exception to on this... well, "type of prop" I guess I should say in that I've applied the same psychology to one of my pet effects. I refer to those bits, like the old Canvas Covered Box, in which a couple of guys from the audience assemble the thing on your behalf.
Trust me, if you have one that's been made the "right" way, there is no way they will find the gimmick and for that matter, there are ways of ringing in the gaffed part of the prop AFTER they've done their work, right under their noses, which makes the thing even more "safe" when it comes to the audience inspection.
My Spirit Cabinet works as well as it does for a similar reason; it is assembled right there on stage in front of the whole world by two dudes from the audience... there's nothing to be discovered! Yet, they haven't a clue how someone obviously gets inside the thing, let alone out without their ever being the wiser (no traps, no mirrors, no bases or silly steps, etc.) It's the psychological fact that I allowed them to touch it all and play with it for quite a bit of time and this fact in and of its own, sells the point to the audience that all is fair.
Kenton has a wonderful Headline Prediction known as THE SECRET COMMITTEE that exploits that very same touch... less being more... or, as it were, confirmation being assumed in that no validation is directly required.
Because of the approach made by our fore-parents in this business, we think we need to build the better mouse-trap with each effect... more gauze and coins or tape for the blindfolds or using steel plates to build the escape trunk instead of wood... the list goes on and on and we all seem to not stop ourselves long enough to consider if or not it's over-kill or when our actions are actually taking away from our objective and the effectiveness of the illusion... not the effect but the over-all illusion... the presentation.
These are things we owe to both, ourselves as well as our audience if we are to deliver "our" very best.
