I suppose this depends on the definition one uses for "wealth." My definition has always revolved around net worth, not cash on hand. I think this is how Ramsey uses the term, but I could be wrong. Think about it. If I have two million dollars in cash on hand (in bank accounts, whatever) but have debts of $1.99 million, am I wealthy?
You probably are wealthy in that scenario. If you have the income to service your debt, you are definitely wealthy. Plus, you can pay cash for things rather than go further into debt. Your mortgage interest will be tax deductible. If you wanted to be anti-social, you could hide some of your assets offshore. You could simply be wealthy for many years and then go bankrupt. Cash on hand is really worth having.