Statistics is, classically, more developed in the realm of "applied math" than "pure math" while linear algebra is, again classically, more a "pure math" discipline. The difference in rhetoric you cite falls out of this exactly.
In practice, both have wonderful presence in math both applied and pure. Linear algebra is one form of abstract algebra which is easily one of the most important mathematical disciplines. It's also the characterization and method of manipulating large arrays of numbers in interesting and practical ways. Statistics is the mechanism of interpreting live data under knowledge of uncertainty toward generalization. It's also probably well characterized as a particularly well-behavior substudy of measure theory... the pure mathematical notion of generalized "substance"