Oxidation of acetophenone to benzoic acid
From a SciFinder search, there are ~10 examples of oxidations of aryl methyl ketones resulting in a carboxylic acid using a chromium based reagent (usually dichromate but also chromium trioxide). This suggests the reaction is at least possible, although I think including it in a textbook is unwarranted.

One reaction slipped through my search that is informative (below). Notice that in the presence of a benzylic position that does contain a hydrogen, the methyl ketone is unchanged, while the other group is oxidized.



Taken together, it seems that chromium oxidation of an acetophenone to a carboxylic acid is slower than alkyl benzylic oxidation.