Whether a good is a Giffen good should be based on circumstance?
Yes, whether a good is a Giffen or inferior good depends on "the circumstances", or to be more narrow, it can depend on the income and price levels.

Claim 1. Being an inferior good is a local attribute.

Proof. Suppose a good $x$ is inferior for all income levels $I$ and all price vectors $\mathbf{p}$. Trivially demand for $x$ at $I = 0$ is 0. If $x$ is inferior for all income levels, then for any $I &gt; 0$ demand for $x$ is also 0. This contradicts the strict definition of inferior good, which specifies that as $I$ increases $x$ should decrease.

Claim 2. All Giffen goods are inferior goods.

This is covered in some detail in textbooks, usually in a chapter that mentions the "Slutsky-equation".

Combining the two claims we have that being a Giffen good is also a local attribute; as being Giffen everywhere would imply being inferior everywhere, and we have shown that that is not possible.