DFW controller providing OJT failed to correct the developmental controller during an inappropriate point out procedure from another sector resulting in a technical airspace incursion.

Narrative

I was conducting OJT on the Local Assist East 1 when the Dallas North TRACON called to initiate a point-out on Aircraft X; inbound and landing ADS. The DN controller stated '8 miles north; Aircraft X; left downwind at 3000 for Addison; if you'll say 'point-out approved' '--which my trainee did after quickly scanning the RACD for the aforementioned aircraft--although the developmental did NOT actually see the radar target or data block of Aircraft X. The DN controller then hung up the land line. Within 2 minutes; Aircraft X was visible on the RACD as described by the DN controller; and coordination was ensured with LE-3. Recommendation; as soon as the developmental stated 'point-out approved' to the DN controller; I should have immediately said 'DISREGARD; UNABLE POINT-OUT; WE DO NOT SEE THE AIRCRAFT'. But reasonably expecting the flight path of the aircraft; I instead opted to observe the developmental begin to panic as he realized that he had approved a NON-observed aircraft to enter the airspace without any idea where the aircraft actually was. This action; on my part; was totally unacceptable and I realized this almost immediately. While the learning lesson was valuable; my choice of implementing it was terribly POOR and risky in itself. In the future; I will utilize 'chalk-talks' during OJT debriefs to depict the consequences rather than allow a potentially unsafe situation to develop into something further; even if I'm confident that it will be safely completed and resolved.