Today I was taught that since the height of a heap cannot exceed $\log n$, it is $O(\log n)$; height in my class was defined as the maximum number of steps in a simple path from a leaf to the root. That is fine, but I think we should further specify it as $\Theta(\log n)$ since it, at that same time, must be greater than $\log n - 1$, and hence also fits $\Omega(\log n)$. I suggested this after class, but I was repeatedly told that $O(\log n)$ was correct, and the correctness of $\Theta(\log n)$ was not explicitly confirmed.
Is $\Theta(\log n)$ correct? If so is there a common reason / justification to just use $O$ instead, and possibly even to avoid using $\Theta$?
Clarification: it's a binary heap.