The alphabet soup agencies from the US are all represented here in force. The DEA & FBI operate with a degree of autonomy that surprises me as well as in joint DR operations. Your CIA/NSA spooks are less visible but can be seen if you shine a light into the right dark corner. The US Marshals have a fugitive contingent stationed here. The coast guard has dedicated docking berths. The US military is stationed here for "training purposes" as is their equipment can we say DRONES?
The US has direct access to immigration records and real time flight manifests as well as banking records (and thanks to FACTA so does the IRS stateside). I am sure these agencies have access to a lot more than we will ever know and operate with the same ease as if one was standing in downtown Happyland Oklahoma. Your obligation to comply with the requests of US authorities here when not accompanied by their DR counterparts is questionable. Refusing to comply would probably prompt the arrival of a DR uniform in short order and would certainly create a note o\in your file somewhere prompting even more scrutiny in the future. Thankfully, US authorities around the world still tend to focus on US citizens for their poop & scoop operations unless drugs, money laundering or that all to nebulous "terrorism suspicion" come into play.