Whether environments are the same or not is based on symmetry considerations and not the number of hydrogens attached to the adjacent carbon atom.
Molecules and atoms within a molecule can be of three types:
- identical - they can be interconverted by simple rotations or translations.
- enantiotopic - they can be interconverted by reflection in a mirror or about a center of symmetry
- diastereotopic - they cannot be interconverted.
Molecules or atoms within a molecule that are found to be identical are said to be in the same environment. Molecules or atoms that are identical, or in the same environment, must be identical with respect to all chemical and physical properties. These properties would include chemical reactivity, spectroscopic environment, etc.
In benzophenone, I can rotate the benzene ring about the $\ce{C5-C7}$ bond. This rotation interconverts $\ce{C4}$ and $\ce{C6}$. If I told you to look away and I performed this rotation (and we removed the numeric subscripts), there is no way that you could tell if the original carbon or the other carbon was now in the $\ce{C4}$ location. These two carbons (and their attached hydrogens) are therefore said to be equivalent by the above definition. The same applies to $\ce{C1}$ and $\ce{C3}$, they are also equivalent to each other, or in the same environment.
I can also rotate the molecule around the $\ce{C7=O}$ carbonyl axis. If I do this I can interconvert $\ce{C4, C6, C8, C_{10}}$. This same rotation also (separately) interconverts $\ce{C1, C3, C_{11}, C_{13}}$, and also (separately) $\ce{C2}$ and $\ce{C_{12}}$.
Therefore, these 3 sets of carbons
- $\ce{C4, C6, C8, C_{10}}$
- $\ce{C1, C3, C_{11}, C_{13}}$
- $\ce{C2, C_{12}}$
are different (diastereotopic) from one another (I can't interconvert $\ce{C4}$ and $\ce{C_{12}}$, for example). So we have 3 different chemical environments, but within each environment there are several identical atoms. The same methodology and reasoning applies to the hydrogens attached to these carbons. They also exist in 3 different environments, and within each of these 3 environments there are several equivalent hydrogens.
