One might possibly get civil damages on that basis (although quantifying the exact alleged 'loss', if any, would be far from straightforward). However, you were talking about fraud, a criminal offence, and I don't think that one should be convicted of that unless a court could be convinced that you made the incorrect statement with the intent of thereby obtaining a pecuniary gain.
I think it's similar to the reason that so many people are prosecuted for 'taking and driving away' vehicles. A successful prosecution for the more serious offence of 'vehicle theft' requires a court to be satisfied that the perpetrator had an intent to 'permanently deprive the owner' of the vehicle - often difficult to prove (except in the case of 'professional' car thieves, if one can demonstrate that they have sold the stolen vehicles) and, in the case of many of the youngsters who nick cars, often not even true!
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