UNIX borrowed the hierarchical file system from MS-DOS?

Interesting statement:

The hierarchical file system -and some other features of MS-DOS 2.0- were borrowed from an operating system named UNIX, which was developed in the early 1970s at Bell Telephone Laboratories largely by Ken Thompson (born 1943) and Dennis Ritchie (born 1941). The funny name of the operating system is a play on words: UNIX was originally written as a less hardy version of an earlier operating system named Multics (which stands for Multiplexed Information and Computing Services) that Bell Labs had been codeveloping with MIT and GE.

(Petzold: p. 333)

UNIX borrowed the concept of a hierarchical file system from MS-DOS? Is he sure? As Petzold himself says, UNIX was developed in the early 1970s and MS-DOS didn't see the light until the 1980s. Was UNIX working without any file system until then? If it wasn't a hierarchical file system, what was it then? I find it quite difficult to believe that Petzold's statement is correct, especially since UNIX and a deeply hierarchical file system have come to be almost synonimous over the years, which cannot be said Microsoft's MS-DOS-derived products. When searching around, all I find is references to Apple's HFS —as, for example, in the link above—, but little or nothing about the general notion of a hierarchical file system. Was it then invented by Apple? No idea, but Petzold's statement sounds quite suspicious to me.