Are all proof techniques which only look at black box behaviour of a TM relativizing?
A theorem about an oracle Turing machine $T^A$ (where $A$ is the oracle) is relativizing if it is of the form
$$\forall A \,.\, \phi(T^A)$$
We say that the statement $\phi$ relativizes. There is no requirement on how such a statement is proved, i.e., we do not assume that we only observe the "black box" behavior of $T$ or anything like that. In fact, it is clear that this cannot be the case, as one can easily prove a relativizing theorem about Turing machines which speaks about how the machine works.

Often we start with a theorem about an ordinary Turing machine, and later we ask whether the theorem relativizes. This just means that we first proved $\phi(T^\emptyset)$, and now we wonder whether the trivial oracle $\emptyset$ could be replaced with an arbitrary one $A$ so that we get $\forall A \,.\, \phi(T^A)$.