ATC could have used "runway 27 approved as requested".

2-1-18. OPERATIONAL REQUESTS
Respond to a request from another controller, a pilot
or vehicle operator by one of the following verbal
means:
a. Restate the request in complete or abbreviated
terms followed by the word “APPROVED.” The
phraseology “APPROVED AS REQUESTED” may
be substituted in lieu of a lengthy readback.
PHRASEOLOGY-
(Requested operation) APPROVED.
or
APPROVED AS REQUESTED

The big issue here is that the pilot requested an operation that will involve getting on the runway, starting a takeoff roll, and then stopping on the runway. The controller issued a clearance that would normally be issued to a landing aircraft. Should raise questions. Is ATC even talking to you? The controller may have mistakenly used the wrong callsign, and is actually clearing another aircraft for "the option". I personally wouldn't move until we(ATC and pilot/crew) came to a mutual understanding of the requested operation and ATC used some sort of verbiage that assurred me they understand and are approving my possibly lengthy occupancy of the runway. Opportunity to help educate a controller and your student, prevent a pilot deviation or avoid a real close look at the bottom of an aircraft executing the "option". Having said all of that I have heard it used many times just as you described. After 26 years of ATC I have also heard "what the hell is that guy doing", "I didn't clear him to for that", "Call the tower, advise ready to copy the number".