I both stand and sit corrected! Listen, I can't be right 100% of the time.
Note to self: No more errors until 2013.
You were right in the first place. MDF isn't waterproof any more than wood is. But,it doesn't swell up when wet. I have used it indoors and out with no problems. Wood trim for exteriors is MDF. Most wood strip siding is MDF. I have use MDF for tomato stakes and it didn't swell even though it was damp or wet all summer.
The problems with MDF are that it will take a permanent set if it is stored so it is bent in any way, I doesn't hold ordinary screws very well at all, and most of the tensile strength is in the hard surface layer, so some joints won't work well. You can't use a piece of 3/4 inch thick MDF as a shelf unless it is supported every foot or so, or it will permanently sag. But, if the load on a MDF part is all vertical it is as strong as most wood. If you cut a groove across a MDF panel (for a tongue and groove joint, for example) the panel is very weak in bending at the groove location.
About high quality plywood: oak veneered plywood can be as poor quality as non furniture grade plywood, and the veneer is only about .010 inch thick, so it adds no strength at all. Birch veneered plywood is far superior if you plan to paint it, since the wood doesn't have large pores like oak does. Birch plywood made of all birch plies is the best there is - often referred to as Finish Birch Plywood (from Finland) or Baltic Birch Plywood (from the Baltic States) or Russian Birch Plywood, the cheapest I have found.