What's damaging to his reputation isn't pursuing the invoice based on an oral contract. What's damaging to his reputation is if he jumped the gun, whipping up drama about a receivable that he reasonably could have expected to get paid if he simply invoiced persistently.
I suspect this thread might be a bit of a litmus test for people who have done a lot of freelancing. From working with designers a bit, I can tell that this is a hot-button issue for them: a lot of clients do shirk payment, and so they tend to insist on upfront payment of some sort before they commence work. But having said that, I have to believe every freelancer is familiar with delayed payments on invoices. Your most lucrative clients might pay many months late, and then only after persistent reminders.