I have only a vague idea based on your question of the situation so forgive me if I'm not hitting the details correctly.
Here's what I guess from your question: You're purchasing a home and you applied for a mortgage. Your Lender's appraisal came back less than the agreed upon sales price. Now the Seller or his real estate agent want you to apply to a different Lender who apparently claims his appraisal will meet the sales price.
If that is correct, here is your correct course of action:
1. You do not have to apply to another Lender. Your Lender's appraisal is sufficient.
2. You and your Seller have the option of working out the price: you either bring more down payment into the transaction or your Seller agrees to sell you the home for the lower, appraised value. Or you both split the difference somewhere in the middle. This gets you a closing.
3. If you and Seller cannot agree on the pricing then you cancel the transaction and call it a day.
4. As for reporting the other Lender, there is a mechanism to do that but first you'd actually have to have made the loan application. Reporting someone because he "says" the value is 4-5% higher won't get you anywhere. Mortgage professionals have opinions on property values all the time. It's only an opinion. No one can guarantee a valuation with an appraiser. Even if you switch and the new appraisal matches what the Loan Officer says, you'd still have a difficult time proving malfeasance. Not worth your time or effort. Focus on making your deal work with what you have or move on.
Appraisals have been coming in VERY CONVERSATIVE lately.
That being said, your main concern has to be that the home appraises for at least what you offered to purchase the home for. If the appraisal does come in higher than your offered price, that does not mean you will have to raise your offer.
As long as the appraisal is at least what you had agreed to pay for the home, you will be ok.
Do not feel pressured to pay more simply based on the appraisal. Remember it is in your best interest not to pay one dime more than the home is worth.
Best of luck to you.
Kawain Payne, Realtor
"guaranteeing" that the second appraisal will come in higher could just be just be a little bravado, to get the business.
I don't see what you would report the lender on, since you said "oh no!" It doesn't seem like they have actually done anything except try to get some business.