The FAA police restrictions are not necessarily a total straight-jacket. As Ken's first link states (p.13):

In addition to the exemptions previously discussed, there are other authorities that waive the prohibition on assistance to police forces of foreign countries. For example, the President may authorize foreign assistance when “it is important to the security interests of the United States”. [13] This allows the President to waive any provision of the Foreign Assistance Act of 1961, including section 660.

[13] 22 USC 2364.
This area of contingency operations law is indeed a quagmire. It starts with basic rules, then exceptions to the rules, and then exceptions to the exceptions. Much of this is due to the interplay between Congresses and Presidents, present and past. In some (many ?) cases, the reason for the rule no longer applies.