Point 1: The police have nothing to do with it - sale of goods at an auction is largely civil matter and nothing to do with the criminal remit of the police. Contrary to popular belief there is no actual crime of 'fraud'. Fraud is category of crimes such as 'obtaining a pecuniary advantage by deception' under the Theft Act. Some form of deception would have to be proved. None of these relate to genuine sales of goods, even if the goods have defects. In reality the police simply won't get involved.
Point 2: In terms of civil law the evidental rule is 'he who asserts must prove' - i.e. the buyer must prove the defect - If he is not showing you a picture of the alleged damage then some suspicion has to be raised that he is not telling the truth - keep your emails and print them out show you can demonstrate his refusal to prove his case.
There are a whole bundle of implied terms under the Sale of Goods Act 1979 - the most important being s.14 - which states that goods must be of satisfactory quality. With regard to second hand goods such as guitars sold on ebay the test is the standard the a 'reasonable man' would regard as satisfactory - so scratches, chips and dings are likely to be part and parcel of a second hand guitar.
But the main poin is this - s.14 only applies to goods sold 'in the course of a business'. So s.14 doesn't apply to a one off sale of a guitar by a private person. Unless you sell on ebay regularly, there is unlikely to be any implied term as to satisfactory quality.
As to misrepresentation - what representation did you give? A misrepresentation must be a representation of past or present fact - you can't make a representation from silence.
As to the credit card company - under the consumer credit act 1974 they are in fact the legal purchasers of the goods and so have a contract with you. They may therefore be liable to repay the buyer.
Your buyer maybe trying to blag his money back from the credit card company and leave them to sue you (I doubt they would as there is no recovery of legal costs in claims under £5000 and so it would not be cost effective). As said above I would therefore keep all correspondence to show that you asked for proof of the defect and that is was refused, that your ebay pictures show no crack and that you did not sell it in this condition.
