RAM integrated brake controller has 'sway control' built in, if it detects sway it'll apply trailer brakes to correct. So in that respect sway and brakes can be related, however OP notes no brake controller... so no clue what he's talking about.
Perhaps the 'tow package' come with heavier ANTI-sway bar(s)?
Found this:
Class-IV towing hitch receiver,31 ATF cooler (not available on M/T), engine oil cooler, power steering cooler,
130-amp alternator, 4- and 7-pin connector with converter, and Trailer-Sway Control (TSC)(V6 only)
The footnote on that is just legal disclaimer, don't tow over limits..etc. I think the only way it could have trailer sway control would be via integrated brake controller, or perhaps they're relying on electronic stability control on the vehicle to control trailer sway (stupid idea I think)?
And found this article on the subject:
Toyota Trailer Sway Control which makes a provably false statement: "Then if automatically applies brake pressure to the individual trailer wheels." (spelling error in original article). Found another reference that states is applies braking to individual wheels (on the TV not TT).
So the system will use your TV brakes to try and control trailer-sway. IMO that's a terrible idea, unless towing a really light weight TT..