How substitutable is Statistics for Mathematics in graduate admissions? In some undergraduate programs, "Statistics" courses (including probability) are listed under the "Math" department. In others, they are "cross listed" with Math courses. And in some others, they are listed as entirely separate disciplines.

Switch over to the admissions department of an American graduate school, with distinctly separate Math and Statistics departments. The informal requirement for admission to the Math graduate program is ten Math courses. But a particular candidate (yours truly, perhaps), has "only" eight math courses, but two statistics courses also. If you treat those as "math" courses, the candidate has ten. The relevant GPA is 3.5; four A's and four B's in Math; one A and one B in Stat. The candidate's GRE score is about 60th percentile for your program; letters of recommendation are solid, but not outstanding.

How might various American graduate programs look upon an application where two statistics courses "replaced" two math courses? Suppose it was four statistics courses; two As and two Bs? People in your school believe that Statistics is "soft" Math, but in the latter case, the candidate has two "extra" courses, FWIW, and maybe some extra preparation and demonstration of dedication.
This can only be answered by the university in question, probably at the level of the math department. It might depend on the specific statistics courses that you want math credit for. As you say, statistics overlaps with math a fair amount and many of the courses depend on a mathematical outlook and way of thinking. 

In general, though, I think you are more likely to have them accepted than rejected, but you still have to face the fact that there will be a lot of other applicants for whom no exceptions need be made. So in a competitive place it might be the competition with those having a more standard background that will work against you. 

But you have to ask them, and, as usual, you need to make your own case for why you will be a success. The evaluation depends on many things not just a bit of bookkeeping.