Which is the falsehood, that the law does not allow "tied sales"
requirements in a warranty, or that there has to be another supplier
out there than Chrysler/Mopar?

Look at the magnuson Moss Warranty act.
It SPECIFICALLY outlaws

""Tie-In Sales" Provisions
Generally, tie-in sales provisions are not allowed. Such a provision
would require a purchaser of the warranted product to buy an item or
service from a particular company to use with the warranted product in
order to be eligible to receive a remedy under the warranty. The
following are examples of prohibited tie-in sales provisions.

In order to keep your new Plenum Brand Vacuum Cleaner warranty in
effect, you must use genuine Plenum Brand Filter Bags. Failure to have
scheduled maintenance performed, at your expense, by the Great
American Maintenance Company, Inc., voids this warranty.

While you cannot use a tie-in sales provision, your warranty need not
cover use of replacement parts, repairs, or maintenance that is
inappropriate for your product. The following is an example of a
permissible provision that excludes coverage of such things.

While necessary maintenance or repairs on your AudioMundo Stereo
System can be performed by any company, we recommend that you use only
authorized AudioMundo dealers. Improper or incorrectly performed
maintenance or repair voids this warranty.

Although tie-in sales provisions generally are not allowed, you can
include such a provision in your warranty if you can demonstrate to
the satisfaction of the FTC that your product will not work properly
without a specified item or service. If you believe that this is the
case, you should contact the warranty staff of the FTC's Bureau of
Consumer Protection for information on how to apply for a waiver of
the tie-in sales prohibition."

So, If any manufacturer other than Chrysler/Mopar produces a fluid
that meets or excedes the published specifications of ATF+4, Chrysler
can NOT refuse warranty based on the use of non Mopar fluid.

As for the "nothing but Mopar ATF+4 meets the spec", I strongly
suspect that is pure bunk. There are ATF+5 fluids on the market that
excede the spec for MerconV, Dextron III, and ATF+3 and ATF+4.
These are synthetic based fluids.

They can be used in place of virtually any petroleum based hydraulic
fluid.
This excludes the obvious, like automotive brake fluids, and the not
so obvious, like Type F Automatic Transmission oil., but includes
white hydraulic oil as used inagricultural equipment transmissions and
hydraulic systems.

Also, the "universal" tyoe A hydraulic fluid is approved for top-up
use in all dexron, dexron II, Dexron 3, Mercon, Mercon V, ATF+3 and
ATF+4 systems.
Definitely NOT to be used with type F