It is theoretically DL's decision as to whether it will permit you access to its priority lane. If indeed the line minder is a DL employee or contractor (doesn't really matter), this is an issue for DL.
Two things of note:
1. Access to priority lines is controlled by the air carriers, whether directly or through a contractor or through the airport authority. TSA does not get involved until the podium.
2. While the Pre-Check lane may be physically longer, it is estimated that Pre-Check moves 6-7 passengers for every passenger moved through a standard lane. Be really sure that despite length, that Pre-Check is not faster. Lite at the standard priority lane doesn't really affect this because it only takes one non-Pre Check pax ahead to slow down the line.