"The minimum Clift is a negative AOA value"  means that positive lift is still being generated at a negative angle of attack.  Go to Airfoil Tools on the net and study the graphs.  Many cambered airfoils do this.

For aerobatic planes, symmetrical airfoils are used to get similar lifting properties when trying for sustained inverted flight.  They will generally will have 0 lift at 0 angle of attack.

So "negative" or "positive" lift really depends on which direction you want the WING to generate lifting force.

For example, if you enter a loop, you may be inverted but still pulling back on your stick to complete the loop.  AOA is still positive.  However, if you do a half loop and wish to fly straight away inverted, you now push your stick forward, to negative AOA, creating lifting force towards the bottom of your wing (which is now "up").

If you then half roll back to upright, you then pull the stick back for positive lift.
This is the "Immelmann" maneuver, from early in the last century.