Core training is necessary, but core training is a lot more than spinal and hip flexion. It is bracing/static stabilization of the spine (think planks), trunk rotation, trunk antirotation, truck rotation+flexion, lateral flexion, extension, and to some degree, hip extension. The movements you mentioned you do for your abs are all hip-flexor based hip flexion and spinal flexion. This creates an imbalance.
The guy is actually correct, and I have been saying this for some time.
Here's whats happening when you do a typical "AB" workout that is predominantly hip flexion:
http://mattsiniscalchi.files.wordpress.com/2011/08/anterior-pelvic-tilt21.jpg
This actually leads to the rectus abs themselves being in a constantly stretched position (among other negatives to the spine and hips). Overtime, it weakens the abs.
If you are going to do those movements, you need to balance them out with movements that return the hip to its natural position (i.e,: movements that target the recuts abs and the glutes)
http://www.webbfitness.net/wp-content/uploads/2011/07/posterior-pelvic-tilt.jpg
In my opinion leg raises should be avoided by most people.
Ab crunches can be modified to make sure you are actually using your abs:
1. Do them on a swiss ball.
2. Contract your glutes real hard before each crunch. This will tilt your pelvis slightly posteriorly, and ensure the hip flexors are not doing the work.
3. Squeeze your ribs toward your hips. Its a small ROM, about 2-4".
4. Add resistance via bands or cables.
Br