I love that logic... and unfortunately, it is not unique.  I had a similar problem with a different client last year.  After sending them past dues notices for many months, we finally told them we would not complete any more orders until they paid the delinquent amount on their statement.  They asked us to fax it over with the invoices, and we did.  Their reply: "Well, sorry, these are more than 90 days old, we can't pay anything more than 90 days old."  They have found some one else to do their work... good riddance. 

That must be the latest scam; ignore the statements for 3 months and then claim that they are not responsible because they are "too delinquent".  Maybe that makes sense to someone, but not me.  Fortunately, it was only around $150 so I was just as glad to see them go.

Best of luck,
Robert A. Franco
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