"The attackers, .. say that attempting to fix the master boot record won’t decrypt the ransomware, and may result in the purchased decryption key not working."
"It is important to note that there is a lot of bad information on the web about how how to fix your computer when it has been encrypted by Petya. Many of these sites state that you can use the FixMBR command or repair your MBR to remove the infection. Though this will indeed remove the lock screen, it will not decrypt your MFT and thus your files and Windows will still be inaccessible. Only repair the MBR if you do not care about any lost data and want to reinstall Windows."
Yes, you can use data recovery tools that ignore the MFT (ex: Recuva) and have some success in recovering files, but don't expect to get them all back intact.