The scenario is this, a somewhat valuable card (let's say it's not power) is misprinted in a particular fashion so as to look "less than kosher." Maybe it's faded wrong or something. Does a judge have the authority to remove the card from the sleeve to inspect it, or do they need to ask the owner to desleeve the card to inspect the card back or something (make sure it wasn't printed on black card stock). More importantly, what about the cards that are misprints and have upside-down backs, or blank backs.
This is really more of a legal issue as far as property. The cards are the player's property. A judge doesn't have the authority to do anything to those cards without the player's permission. However, deck checks (whether random or checking a specific card for a specific purpose) are part of events. If a player refuses to allow someone else to examine/handle their cards, they would likely not be able to participate in the event. And if the judge concludes the player is refusing to allow his deck to be checked because he's cheating, the judge can DQ him. So basically to complete the event you need to give the tournament staff permission to examine your cards as they see fit. And the argument could be made that you already do so implicitly simply by participating in the event.
We were wondering whether it was a good idea to take those cards to tournaments such as gencon.
Any time you're taking any sort of modified, misprinted, or somehow irregular cards to an event it's a good idea to have backups. It is entirely at the head judge's discretion whether to allow a modified or misprinted card. So if you're planning to try to use it, ask the head judge before the event and be ready in case the answer is "no." ("It's my only copy" likely won't sway the judge).