As the local home buyers and Realtors will attest, California, by and large, is in a sellers market, at least temporarily. The "banks" are trickling out their inventory and based on the positive effects of multiple offers, see no reason to cease this action.
As for bidding above the value, many are actually using this as a technique to get their offer noticed. Since most offers are presented with an appraisal contengency, it doesn't matter if you bid 100k above, you'll get to re-negotiate once the appraisal comes in. Chances are, the seller will agree to sell the home at appraised value rather than accept a back up offer and have to go through the negotiating process again.
Some listing agents have become savy to this and are attempting to explain this to their asset manager. However, since many asset managers are lacking experience, this can also be a difficult task. This also explains why the lender/servicer/bank/asset manager (Or anything else you may wish to call them), seem to do things that are contrary to logic.
There are a few who will pay cash above the market value due to the fact that they believe the market has hit bottom and they wish for that particular home or neighborhood, or an investor has factored this into their overall strategy in the aquisition due to local rents being high enough to help in the financial justification of such action.
In closing and in simple terms, a lender will only lend based on appraised value, or aquisition price, whichever is less. Any other monies would have to be paid for in cash and be considered in the loan request in case this action affected the reserves the loan approval considered in the original underwriting decision.
Best of luck and don't worry, more inventory is on the way.

Amaya,

There are too many variables to give you a firm answer. Most times when an agent tells you it will not appraise, it means you offered too much for the property and you will not get a lender to loan you that amount because the value of the property is less than what you are asking the bank to lend you.

You may get the house, but why would you want to overpay in this market? If the house is lower than the market value for the area you may be ok. If the house is priced at market value and you go over that, it may in fact not appraise out and you will not get the loan.