As Mike Florio of Pro Football Talk pointed out, the NFL does have a say in every playing surface that its teams play on.
In addition, a league source said the NFL officials is engaged in the field maintenance and management of Soldier Field, just like every other stadium. That, I'm told, is a constant line of communication that's open.
The Bears and the Chicago Park District determine the playing surface at Soldier Field. But, the NFL could weigh in on the debate, natural grass versus FieldTurf.
Here is what is written in the NFL Game Operations Manual:
"Each home club is responsible for having the playing surface of its stadium well maintained and suitable for NFL play. The League may require improvements to ensure compliance and such improvements will be at the Club's expense. Failure to maintain a playing field properly is considered a competitive issue and clubs that fail to do so may be subject to discipline."
In other words, the league has the final say on whether a field is suitable or not.
The manual also says: "It is prohibited for Clubs to change from one playing surface to another surface during the season without discussing the change with and obtaining the permission of the League office. This has been further clarified to include artificial turf to artificial turf, grass to artificial turf, and grass to grass. The NFL Game Operations department must be informed and permission must be granted prior to any change."