This is what I do for a living, and have for decades. The above is exactly right...except for asking for the names of dealers that have your exact car for $11k, the insurance company doesn't need to do that, and won't. Almost all auto policies are actual cash value, not replacement cost. If you feel the valuation is wrong, you need to explain why. What options did they miss? Is the mileage reading right (how many miles are on it??)? Look through their valuation report carefully and see if anything is missing or wrong. No, they wouldn't use Edmunds typically. Make sure you have a copy of the report...more than likely it's either from a company called CCC/Valuescope or maybe Audatex.
Honestly, without knowing a lot more about your car, I don't think they're that far off...a '14 Camry SE sells right around the $11k ballpark on dealer lots (they don't owe you dealer price, they owe you retail value). But like I said, I don't know how many miles you have on it and what geographical area you're in. I know you paid a lot more, but yes, the Camry does depreciate.
Any questions, let me know.
Don't really want to get off topic of helping OP. Like I said, I agreed with nearly everything you said, except one small point. In this case, Camrys are on every street corner, so any valuation will include a very large amount of "comparables". However, sometimes current comps can't be found, so it's based on historical data (usually a less common car), or a car that's not exactly the same...and adjustment are made to account for the difference.
