Stats is not maths? How mainstream is the claim that stats is not maths? And if it's right, how many people don't agree? 
Given that it's all numbers, taught by maths departments and you get maths credits for it, I wonder whether the claim is just half-jokingly meant, like saying it's a minor part of maths, or just applied maths.

Statistics can be thought of as an application of mathematics towards the rather specific goal of examining numerical data.
In order to understand statistics, you should probably know some mathematics. In a similar manner, in order to understand engineering, you should probably know some mathematics.
But just like in engineering (or any other applied field), there are domain-specific definitions, terms, and conventions that arise extrinsically from mathematics. For example, the $p$-value is a concept that arose to make sense of data. It can be mathematically studied, but it did not necessarily arise as a natural extension of some prior mathematical definition.
