An interesting question.
Your original quote had the adjective "accurate", not the noun "accuracy". English adjectives are either "gradable" or "non-gradable". Compare "cold" with "married": you can be more "cold" or less "cold", but you either are or are not "married". Some adjectives are, purely by convention, normally considered "non-gradable", such as "stationary".
So your supervisor's point is not that the noun "accuracy" is binary, but that the adjective "accurate" is non-gradable.
I have to admit, that to me, as a native speaker "more accurate" sounds fine.
For the noun "accuracy", the Oxford Shorter Dictionary gives the following definition.
1. The state of being accurate; precision, correctness.
2. The degree of refinement in measurement of specification, as given by the extent of conformity with a standard or true value.
Of course, you are thinking, quite correctly, of the second definition of the noun. However, for the adjective, it says the following.
1. Of a thing or person: exact or correct, as the result of care.
2. (Obsolete) Executed with care.
3. Of a thing: in exact conformity with a standard or with truth.
So, from those definitions, it sounds like a non-gradable adjective. Your supervisor, although s/he disagrees with you and me, might be able to claim some authority for the proposition that you cannot say "more accurate".
Since this is a supervisor, and there appears to be at least some difference of opinion, perhaps you should compromise by rewording it to "it is not possible to tell which set of data has a a higher level of accuracy."