The thing is, not all brokerages supply you a 1099-B according to IRS requirements,
TD Ameritrade, for one, reports a short sale as described, above.
Some brokers will make date disposed equal to date acquired.
If your gain/loss totals are accurate, and TurboTax passes it, I expect you can file that way.
References:
IRS Instructions for Form 8949,
"Column (c)—Date Sold or Disposed Of
Enter in this column the date you sold or
disposed of the property.
"For a short sale, enter the date you delivered
the property to the broker or lender to
close the short sale."
That would be the settlement date after acquiring the property.
