I also have a bit of experience in traversing mud, muddy bottoms, and mud flats. (Landing Craft, don't you know). Sorry KD5NRH but that's pretty ignorant. I get that you've done it, but it's a bad idea. Submerged mud isn't actually always buoyant. That's why it is submerged.
If it's submerged, then a) it's more buoyant than water and b) there's this other stuff on top of it that's exactly as buoyant as water. Roll over. You can't even get the swimming merit badge without knowing how to float on your back.
Yes, I suppose floating on your back in water could be an absolutely horrible idea on the chance that the laws of physics might suddenly change dramatically. OTOH, I can't find any documented incidences of that in recorded history, so I'll risk it.
Where I grew up in AK we lost a handful of people per year when they got stuck in tidal mud, and the tide came in.
Since you're familiar with the pond in question, what exactly is its tidal range? I know I once spent nearly 20 minutes stuck in a hole with water to my rib cage, and somehow managed to avoid drowning, so I'm doubting that even getting stuck hip deep would have been a real threat, considering that if it's the pond I'm thinking, the spring tide range could be a few microns.
Then assuming you get there, you get to free dive, in the dark,
Considering I can't see underwater without a mask, this is pretty much what 90% of my dives are like anyway.
Then try to get the maybe can/maybe can't panicked kid back to shore and through the dangerous mud.
Well, you know, if you've made the huge investment in a good piece of rope, and remembered to leave one end with the guys on shore, then you get them free of the car and put their hands on the rope. The best plan in any water rescue is to give the victim something else besides you to hold onto whenever possible. It they can't figure the next bit out, then you just move on to the next one and come back to the idiot when you've attempted all three.
I don't blame the cops at all for not going out there for this one.
Maybe it's just the way I was raised, but <10% chance of me dying vs, let's call it 25% chance of saving at least one of the three who would almost certainly die without help, I'm going. Don't really care about their crime for the moment either; last I checked, the death penalty is still considered excessive for 15-16 year old kids joy riding.