The Ninth Circuit has determined that a person who is issued an expedited order of removal at the border has entered the United States for the purpose of the reinstatement provision. Thus, any subsequent re-entry without valid documentation would qualify as an illegal reentry, triggering the reinstatement provision. In this case, the petitioner re-entered the United States as a passenger in a car, but did not have any valid entry documents. Thus, the Department of Homeland Security was permitted to reinstate the previously issued expedited order of removal.
The full text of Tellez v. Lynch can be found here:
http://cdn.ca9.uscourts.gov/datastore/opinions/2016/10/24/12-73424.pdf