Amtrak owns the Northeast Corridor outright, and also a stretch of track in Southwest Michigan. Plus, of course, the approach tracks to stations it owns, such as Chicago or Washington Union Station. The few local freight movements on the NEC (via trackage rights) generally operate at night.
As for the other routes, Amtrak’s Basic Agreement with the freight railroads—and federal statute —explicitly gives them priority over freight trains. Alas, a complex court battle that went to the Supreme Court and back ended a year ago with this provision left unenforceable, and Amtrak on-time performance is now down under 50% for long-distance routes. Details and a proposed legislative solution are on page 47 of Amtrak’s most recent annual report.