This is not true. Mathematicians do not assume that the Hindu-Arabic numeral system is the correct one. There is no "correct" numeral system. It is used as a matter of convention and of convenience. The disciplines of physics and mathematics existed long before people started regularly using a base-10 positional numeral system, and the predating facts did not suddenly change afterwards.
For instance, Euclid proved theorems in elementary number theory without the benefit of our current number system. He discovered properties of prime numbers and wrote them out with words only; the Greek numeral system was alphabetic. Much of ancient mathematics was done this way, and mathematics can still be done this way if we want. Our numeral system does not enable us to do mathematics; it enables us to do mathematics in a systematic fashion.
We don't need the Hindu-Arabic numeral system to prove that the system of real numbers is the unique complete Archimedean field. The real numbers can be constructed without our numeral system, and if we were to actually use a different base, as people in the past have like the Babylonians, then the same properties would apply. Certainly, if humans had eight fingers and eight toes as opposed to ten fingers and ten toes, then we would likely have a base-8 numeral system.
I believe that the mistake you are making is equating numerals with numbers. They are not the same. A number is an abstract thing independent of its "name". Numerals are merely what we use to write them, to represent them with, to "name" them. Don't worry; we haven't left any out!