It would be very interesting to see what would happen if this were to occur in a case where the defendant's phone records were relevant to the defense's case and the defense attorney asked for the NSA records to demonstrate innocence. Not sure if this case qualifies or not, as I haven't heard anything of it other than this article.
The phone company does not have the records anymore, according to the article. So they want to get the records from the NSA because they probably have not deleted them.
In this case they're hoping the NSA kept better records than the phone provider:
"The prosecution had told defense attorneys that they were unable to obtain Brown's cellphone records from the period before September 2010 because his carrier, MetroPCS, had not held on to them."
I really hope that they tried to get the records through a court request to the right people rather then just calling the company and asking for it. I find it really unlikely that such records don't exist anymore. Phone call billing is the one thing that brings money to telcos and they're often processed and analysed. They may not be exposed to public, but not keeping a backup of them stored at least on some tapes somewhere for years is really surprising...
The NSA database is made up of records from phone companies, per the Verizon FISA warrant. This story does not concern the recording of conversations, but records of calls made. Of course, the appellant's contention is probably specious but that's not unusual in criminal cases.