So, a frequency bin is centered around an interesting frequency $f_0$. Assume the spectrum is such that there is no spectral leakage from other frequencies to that specific frequency $f_0$. Now. I center a frequency bin around f0. The value (magnitude) of this bin is then the value of EXACTLY this frequency $f_0$ and is not affected by non-zero frequency values (magnitudes) of frequencies that also lie in that bin's range. A frequency bin 'only' covers the value of its center frequency (+ potential spectral leaks to that center frequency).
Is that correct?