Without hesitation, computer science is certainly not a mathematics major.
Having some knowledge of some aspects of a subject, doesn't make you qualified in that subject. At least, not at the university level.
Mathematics is an enormous and ancient subject. The maths that a CS student is exposed to is really a very small sliver of a few topics; applied to certain uses. Many other subjects (almost all numerate ones) have a similar relationship to maths.
Consider economics: aspects of it also make use of (applied) mathematics, but no one could seriously make the claim that an economics major, even one who has extensive capabilities in numerical modelling, is basically a mathematics major.
Theoretical CS could be described as "a form of applied mathematics"; but Theoretical CS is only a component of a CS degree; and, from what I see with young graduates today, a decreasingly smaller part of it (I am not making a value judgement - just an empirical observation).