No one else can access your past tax return. Only you can access your account. If you used TurboTax for your 2015 return, you will need to purchase PLUS to get to it and print it or view it to get the SSN's.
Many people have multiple TT accounts and forget how to access them. Log out of the account you are in now.
Or did you use the desktop version of TurboTax? If so, the files are on your own hard drive or any backup device you used like a flash drive.
How do I get a copy of a return I filed using online TurboTax?