I imagine that once again you've overapplied a rule that someone who was simply trying to guide you gave you. Either that, or the native speaker in question misled you into believing that this is an absolute rule, which I find unlikely.
I think you probably should, yes.
Do you mean it isn't wrong to use "sometimes" in a negative sentence between verbs? The native speaker who advised against using it isn't a teacher. That's why I decided to ask my question on UE to receive an answer from an actual teacher. I might have misunderstood their explanation. This is what they wrote: "I don't sometimes drink tea." Sometimes" obviously means some times, so it wouldn't make sense to use that negatively the way your example suggests. When used this way as an adverb of frequency, 'sometimes' sits in the middle between never and always, so you wouldn't just negate it - you'd use a better adverb.
"Some" can by default mean 'not all'. For example, "I go to the gym on some days" would mean you do not go every day. Likewise, we use 'sometimes' in connection with things that do occur, but not very often, so there is also no need to use it negatively to refer to the occasions when something doesn't occur.
Saying "I sometimes drink tea" means you do drink it, but not all the time. If you wanted to use a negative to mean the same thing, you could also say "I don't often drink tea". Of course, if you don't drink it at all you would simply say "I don't drink tea" or "I never drink tea" - there is no need to use an adverb of frequency with something that never happens.
However, you could use 'sometimes' in a negative sense if the thing you were proposing was an alternative to the norm. For example, if you mostly drank tea, but occasionally drank coffee instead, you might say "sometimes I don't drink tea".
Forget the "between verbs" rule, that doesn't exist. As I explained, you could say "I don't often drink tea" and that is just another adverb of frequency. The meaning of 'sometimes' as an adverb of frequency specifically means 'some, but not all', and that is just something which cannot be negated. If something isn't occasional, then it is either more, or less frequent. You would just use a different adverb. –
I have been updating my answer to accommodate the suggestion from anotherdave and also in response to your questions, I hope its clear now. "Sometimes I don't drink tea" would be a useless statement on its own unless you added what you DO on the occasions when you don't drink tea (ie you drink coffee instead). Placing 'sometimes' where you did in your example is what is problematic because you're negating the action, not the drink.
Sorry for the long post.
