Because a company with positive equity isn't bankrupt
The simple version
Equity in accounting terms is a part of the Statement of Financial Position (previously called the Balance Sheet) and represents the value owned by the shareholders. It was called a Balance Sheet because it balances:
Assets - Liabilities = Equity
A bankrupt company is one that is unable to settle its debts meaning that its Liabilities (what it owes) are greater than its Assets (what it owns). Therefore equity is negative - the equity has been lost before the company files for bankruptcy.
Since shareholders have limited liability, they do not have to contribute to pay the company's debts so their shareholding is worthless. Their shareholding can't be worth less than worthless so in that sense David Jones is right “No one ever loses equity in a bankruptcy case, Equity gets lost long before the case is filed.” It is the loss of the equity that caused the bankruptcy.
The more complex version
The Statement of Financial Position is a point in time measure of the liquidated value of the entity - that is, the value of the company if all assets were sold for their book value and all debts were settled for their book value. This isn't something that can actually happen for all sorts of reasons.
A company that gets liquidated will often not realise the full value of its booked assets because these are accounting measures of value rather than sale under the hammer values at a liquidation auction.
Further, businesses as going concerns have a different value than their book equity. An ongoing business will make profits (or losses) in the future and the expectation of these needs to be added (or subtracted) from the book equity. This is why a company with negative equity may still be worth operating and, conversely, why one with positive equity maybe should be closed.
Also, businesses may have significant off-balance-sheet assets such as valuable IP and branding that was developed in house and therefore don't create bookable transactions. For example, there is no item in the Coca-cola balance sheet that represents the value of the brand. This is clearly an item of value that a) isn't on the balance sheet and b) only has value while someone is making cola and using that branding. Kodak, Blockbuster, Panamerican and Concorde were all once valuable brands that now only have nostalgia value.
One final point is that it is quite possible for a business with positive equity to go bankrupt because bankruptcy can be triggered by insolvency. Insolvency is being unable to pay your debts as and when they fall due. An asset rich but cash poor organisation can be insolvent while still having positive equity. For example, a property developer may have a large portfolio of valuable property and owe a relatively small amount to contractors, however, if they can't come up with the cash to pay these debts they are insolvent and this can trigger bankruptcy.
Many businesses and individuals may be insolvent and recover from it - they borrow money from a bank (or by delaying payments to creditors) or inject more funds into the business. It is usually only when a business is of borderline profitability that insolvency will push them into bankruptcy.