It says that the owner may "make or authorize the making of" a copy for this purpose. This means that whether or not the copy is infringing will hinge on the language of the authorization granted by the owner.
It's noteworthy that despite the language of "...or authorize the making of..." being in place prior to MAI v. Peak, the Peak technicians were not considered sufficiently "authorized" to make a copy by running a program that the computer's owners had purchased, even though doing so was a necessary component in fulfilling their duties. One would think that logically, the owner's authorization to make the copy would've applied.
Going back to the decision to see the reasoning on this, I find nothing specific discussing why the authorization from the software's owners would not have applied. [0]
There is some commentary about how in a prior case, copying the program onto "silicon chips", meaning the fixed medium of a diskette (non-floppy), was ruled infringement because it was "not an essential step" in using the software, since it could be used by copying it only into RAM. Since the software could be used from RAM after being read from disk, it was "fixed" copy under the statute.
That's all well and good (not really, but discussed above), but it doesn't say why the authorization of the owners of MAI software was insufficient to allow the computer technician to make copies as his/her agent, necessitating the addition of subsections (c) and (d) in 1998.
[0] https://www.law.cornell.edu/copyright/cases/991_F2d_511.htm#...