Okay I took a look at the actual page in the manual (9-19) that mentions tire chains. What it says is that tire chains (and by tire chains it means the traditional link type chains) cannot be used because there isn't enough clearance and they'll hit parts of the body/frame when you turn the tire from side to side. The exact quote is: "Tire chains cannot be used on your vehicle. The clearance between the chains and the body is not sufficient to allow proper clearance, and the vehicle body might be damaged."
It should be noted that cables are NOT chains! In fact, there are all types of snow traction products that meet SAE Class S requirements (which are specifically designed for vehicles with restricted clearances). These are the products that we'd want to use. Here's an example of one (note that this product does not require very much clearance around the tire, certainly much less than traditional chains with links): https://www.peerlesschain.com/brands/traction-product-choices/super-z/
By the way, if you chain up, put chains on ALL 4 wheels. The law requires just one axle (the driven axle) but these are AWD vehicles and both axles are driven, and though the law doesn't require you to chain all 4, having only 2 wheels chained is extremely dangerous, particularly if you put them up front. It's pretty easy to spin/fishtail if you hit a patch of ice at the wrong time.