I would have to agree with Gordon. Just walk away. In a previous BV discussion (see "Wet Crawlspace by Camille") I discussed various options for moisture, but indicated that standing water is a very different, and potentially expensive matter. Normally, drain pipes are used for basements because basements are essentially holes in the ground that mother-nature continually tries to fill (with water) Crawl spaces usually have the level of the ground under the house the same as outside, so drain systems are not usually necessary UNLESS there is a high water table. Remember, water will always seek itís own level. In Camilleís case, she has the option of correcting her problem by building a whole new foundation. You probably do not have the same opportunity.
In answer to your question about where the drain tile should be located, the idea is to get the water in the soil to drain into the tile (or drain pipe), and not collect under the house. In a basement situation you want it below the basement floor. For your crawl space I think what you described is fine as far as it was designed. In either case, digging below the footers for any reason is not a good idea because the footer should be resting on undisturbed, packed soil so the house does not shift around later.
But, as said before, if you can walk, walk. Water in a basement water is much more common, and more easily dealt with because you can get under the house easier for the repair. Water in a crawl space probably means just like you were told: a high water table. To me, the fact that the house in question has drain tile indicates the builder, or the municipality, knew of the need for some type of drain system. Wet ground will be always unstable, and simple drain tiles, French drains, or whatever, will not really help. Your new house could constantly shift and settle. The problems you may have later could be far worse than just water in the crawl space, and far more expensive than the $5k youíve been quoted.