I give classical and flamenco guitar lessons via Skype. It is realIy only one step removed from an in person lesson, so I see no reason why a student couldn't or shouldn't say that he or she studied with me.
On the other hand, if someone is merely watching generic videos, it seems a bit strained to say that they "studied with" so and so.
I think "studied with" implies a sustained one on one period of study. A good example might be from when I studied flamenco guitar with Mario Escudero. Sabicas, who was Mario's distant cousin, was frequently there when I was having my lesson, (we all lived within five minutes of each other) and so Sabicas taught me quite bit in person, but I would hardly say that I studied with Sabicas.
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