You aren't wrong - just don't have the whole picture. Weatherproofing, depending on the quality of the garment, comes from a combonaiton of several components. The outermost aspect of weatherproofing is the DWR layer - Durable Water Resitant layer. This is typically a spray-on or wash-in liquid fabric coating and is what is responsible for the beads of water you see when you are sitting on the lift. The quality of DWR layers varies greatly and is effected by washing in two ways. First dirt and oils that cling to it will decrease its effectiveness and may allow water to penetrate instead of beading up - so washing will help. Second these coatings will 'sink' into the fabric after time leaving less on the surface to do battle with the weather. The heat from washing and drying will help bring this to the surface again.
The bad news is yes, this coating will eventually wash out - again the wash-out rate will depend on quality. I saw one statistic that said that mid quality DWR coatings should last for about 27 washings. That is a lot of washings in my book. At any rate you are correct about using the right wash - sport specific wash like
G-Wash will go a long way to protect the DWR layer. There are also some products that wash in that will replace or at least extend the life of the DWR to some degree. The key is to buy quality and take good care of it.
As far as the other weatherproofing layers the most common is the waterproof/breathable layer. This is a porous membrane that is either laminated to the back of the fabric or a free-floating layer but either way the pores will stretch and give with use and eventually let moisture through. The action of washing and the exposure to heat and water will cause those pores to reconfigure, re-establishing the like-new quality of the membrane.
Hope you enjoyed your crash course on fabric technology!