If you use their product, per their tos, my understanding is they can train on their customer data at any time. In other words, if you use their product, they automatically have license to train on your art.
I think the only statements saying that they don't train on their customer data is from their CEO, but unless they encode it in their tos, that doesn't really matter.
How do they even get "customer data"? Majority of people in this space do not use Adobe's cloud.
Do you think they just stream any photos you've opened with Photoshop to Adobe?
I mean, given their recent liscence kerfuffle it seems clear to me that Adobe really wanted to be able to train on customer data. They had to backpedal, since that generated a surprising amount of controversy. They hold an effective monopoly in certain fields, and their behavior shows they really don't always have customer interests at heart.
Even without customer data to train on, they do have a pretty large moat with their image library. And you are right, they are in a good position VS competitors who trained on data they don't have rights to. We'll have to see how things play out legally, but I wouldn't be surprised if it ends up that something like midjourney ends up in an untenable position. However, openAI has a huge amount of funds that could be redirected to fight a oegal/lobbying battle. While they aren't a direct Adobe competitor, their whole business revolves around using unliscenced data to train their models, so they have a pretty clear horse in this race.
Someone submits one image to their library that they didn't own the rights to and Adobe has to do a completely new training run to remove it, since you can't just delete.
Or they just leave it up and admit they didn't need the rights and their library being cleared of rights isn't really a value add.
AI becomes a lot more useful in a commercial setting when you can steer it towards a desired style which means training. Would imagine once they roll out the ability to drive it that way they'll include the licence to use whatever you feed into it for their own training too and many will capitulate.
Given that they own a big library of images, it's the path they prefer.