Not at the time, but it is now. It was owned by the Regents of The University of California, and in the intervening decades, it has gone from being a license you had to pay for, or otherwise negotiate, to a generally open source license.
Wikipedia puts the BSD (open source) at 1988 introduction with the GPL being 1989. NeXTSTEP was released September 18, 1989. So, I would say your dates do not mesh and joejohnson's comment is correct.
BSD wasn't completely open source until much later, so I would assume that NeXT purchased a license, just as they did for Display PostScript and other pieces.