For what little my opinion actually matters in this, but I am all in favor of restricting the time players have after a a challenge is issued until the opponent actually accepts the battle. As a host, I find it's a major annoyance that player spend 10/15/20 minutes doing who-knows-what before trying to play. Smogon Tour is live, and while I get you can't spend forever sitting at your computer waiting for your opponent you shouldn't be off doing something else while you're still in the tournament. It's not all that unreasonable to expect both players to be able to play in 5 minutes or so when they get challenged.
Though, on the time-since-challenged policy, you don't actually get a timestamp when challenging someone, so I don't know if a screenshot of the challenge window is feasible (not having timestamps enabled/faking the timestamp by pming them eariler). If this is the route taken, you'll probably need to include the lobby chat in the "proof" for a reference point and pm your opponent right as you challenge them/shortly afterwards. And require people to have timestamps on if they want to make this claim at all.
Though, on the time-since-challenged policy, you don't actually get a timestamp when challenging someone, so I don't know if a screenshot of the challenge window is feasible (not having timestamps enabled/faking the timestamp by pming them eariler). If this is the route taken, you'll probably need to include the lobby chat in the "proof" for a reference point and pm your opponent right as you challenge them/shortly afterwards. And require people to have timestamps on if they want to make this claim at all.