First Off, Assuming that you can knock 25-50% off of the asking price and get it apporved is simply insane. There's too many factors involved that you need to consider before doing that. You're just throwing spaghetti on the wall if you try to buy a house this way.
3rd party appproval does NOT mean that the bank owns the home. If the bank owned it, there wouldn't be a 3rd party that would need to approve the deal. Bank owned homes are called REO (real estate owned).
Don't expect Yahoo's foreclosure site to be completely accurate, either. Even realtytrac.com can be inaccurate, and their source data if MUCH better than how yahoo pulls theirs.
In regards to a bank holding the offer and them claiming another offer came in higher, there are 2 ways to look at it. If an agent is representing them and they tell you this, they risk losing their license if they're lying. Write the higher offer as an escalation clause to the bank and require that they show you the value of the other offers. Then there's no confusion about honesty.
What 3rd Party approval does mean is that the house is in pre-foreclosure and the owner will be taking a loss in selling the home, which is why the bank (3rd party) must approve the sale. Ever heard of a
short sale? This is it! You can usually get a great discount on a short sale, but the property is disclaimed, not disclosed, so Caveat Emptor (buyer beware). Make sure you have an agent that KNOWS how to cover your bases!
Also, Short Sales take time, so don't be surprised if it takes 2 weeks to get a contract ratified, and 2 months to be able to purchse it. Very rarely do I see a short-sale deal get done in less than 30 days. There's simply too many people that have to be involved in the deal (and even more if the owner has a second note on the property!)