It's not really a question of what teams can and cannot. It's more a question of how much HP does your tank have. When you're solo tanking it, the challenge hits a shadow for roughly 1050 damage when it ticks, and it ticks once per second. It's internal damage, so that means the pre-mitigation hit is 1364. That's not too much damage, but you have to sustain that for 20 seconds. Thus, 27280 damage pre-mitigation overall. So, Thiol is losing 22097 HP for each tank challenge. That's not that bad if the other tank is taking the boss back (though I will say that your Jugg tank would only lose 20733 HP, and that's if he never uses Force Scream), but it's still a lot of damage. More importantly, it's completely avoidable damage.
The only advantage I see to solo tanking the challenge is it makes the tanking a little bit easier in the first few seconds after the challenge phase. But as long as your tanks complete their challenge first (something that is easily ensured by coordinating start times), they will be out and controlling the boss well before it becomes a problem. Dual tanking leaves more healing margins (i.e. if a tank gets spiked right before the challenges, there's no need to waste mana that could be spent on the healing challenge) and is good practice for Nightmare Mode, since I'm quite certain it wouldn't be possible to solo tank it there.
This does lead to a rare but significant anomaly. What if (on NiM mode) one of the tanks gets challenged? You send your tank + tankiest dps? What if the tankiest dps does not survive, a sorc with bubble? Unless I've missed something about the challenge mechanic this could cause problems later on.