The suspect, 74-year-old Gary Van Ryswyk, said he met the victim on a eunuch fetish website.
A "Ferguson effect" argument says a pullback in police action can lead to a rise in crime. Experts say there's little evidence of that.
James Bryan Peterson, 54, was arrested after the woman called 911 to say she was being held against her will.
Cases have been reported in 15 states from coast to coast but mostly in the Midwest.
An advocacy group called for an inquiry into families being split up at the border, with parents sent back to Mexico and children sent to U.S. shelters.