as long as the stand is indeed structurally sound, and the ends are EVENLY supported, it's really a non-issue. the problems begin when the two ends are of different angles, then flexing and torsion will break the glass in no time.
a good way to test this is to sit your empty tank on the stand. if it sits sturdily, without any sort of movement when you try to tip it from side to side/front to back, then it will be alright.
Reading in the DIY forum about when to use foam under a tank a while ago everyone was very concerned about a couple inch slight dip in the wood stand so I think I'd not use it like that. How is the rest of the construction? Particle board? Sounds like the trim piece is really holding it together. Glued? Screwed?
The lfs guys have a name for some, "exploding stands" I believe.
i have a metal stand for my 20g that supports only the outer rim of the tank, nothing in the middle. no problems, its been set up for about 1 month. its a bit tilted and im going to fix that but otherwise no problems.
For glass tanks: The tank should be evenly supported around all edges of the tank. If it isn't there will be uneven stress that may eventually lead to a leak or crack. The middle area of the bottom should be open, or resting on high density foam. The glass should not rest directly upon a hard surface, because if there is a small bump or particle between the glass and surface, it may lead to a crack developing.
For acrylic tanks: The full bottom and edges of the tank should be supported. It is recommended that a layer of high density foam be placed between the supporting surface and the tank so that the tank levels itself.