Was the growing medium wet, slightly moist, or dry to the touch when they were falling over?
Wilting can be lack of water, sure, but you'll know it because the media is dry to the touch, for several inches down. But it can also be a sign of compromised roots, such as root-rot, caused by fungus (and usually wet conditions.) This can happen if you water and let water remain in the tray underneath your pots or flats, or poor drainage.
The roots will be brown and not the usual bright white color.
I've found tomato seedlings pretty resilient in dry medium if the wilt is caught quickly and the seedlings watered.
I seldom have problems with dampening-off. Keep your germinating containers clean and use a good seed starting medium.