I'd agree that you should start out by determining your tongue weight. Use a scale, and make sure you have 12% to 15% on the tongue. The other thing to check is that your trailer is level, as riding too far off level will also contribute to sway.
The story on weight distributing hitches is that they are a North American item. Trailer standards developed differently in Europe (lower tongue weights, surge brakes, no WDH) but North American trailers are designed to have a significant tongue weight, and often benefit from a WDH.
Because WDHs are not common in Europe, European vehicle designers recommend against them; they simply don't know anything about them, and how well they work in practice depends on the setup, which the vehicle manufacturer doesn't control (it is up to the owner).
I wouldn't hesitate to use a WDH on an E53, if you have the OE hitch. It is very solid. The tongue weight limits address the use of a WDH. There are two separate points here though. A WDH improves vehicle and trailer handling by essentially moving the virtual CoG of the tongue weight forward, so that it isn't hanging off the rear bumper but instead is between the front and rear axles. The vehicle will handle better, and that can certainly help with sway. But there are also sway control devices that are sometimes part of a WDH, and sometimes separate. These devices essentially damp out the sway, usually with friction (unless you go to a pivot point projection hitch, eg Hensley or ProPride, which are probably more than you want to spend)
The E70 hitch doesn't appear to be as strong as the E53 hitch was. This may be the basis for any warnings. It is certainly strong vertically and horizontally (tongue weight and braking) but it may not be as strong in bending, the levering effect of transferring tongue weight to the front axle of the tow vehicle.
Some of the best research you could do on this would be to go to the CanAm RV web site. The owner publishes towing articles, consults with travel trailer manufacturers, is an acknowledged expert on trailer and tow vehicle setup, and has links to most of those articles on their website.
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Jeff