I don't think this has anything to do with her toilet training difficulties. That's normal in a great number of children.
I don't know your daughter (obviously) and I don't know Dr. Becky, but I do know about irrational fears. Your daughter most likely isn't doing this for attention, or just being dramatic or overly sensitive. She has an irrational fear, it's anxiety provoking, it's obsessive, and it's real (to her, anyway.) You can reassure her that nothing will come out of the toilet at night until you're blue in the face; you can show her a plumbing diagram of toilets and how it's all one-way-only, and she will understand, but she will still have that fear, because right now, that's the hiccup her mind is having. I commend you for consoling her instead of dismissing her fears, and for asking for help.
Everyone has irrational thoughts, but for many, they are quickly dismissed or forgotten. Maybe it's the age, and as your daughter is of the age when "monsters under the bed" type thoughts start, it might just be that. How you react - emotionally available and not dismissive - is important.
First, please familiarize yourself about irrational and intrusive thoughts in children. When you understand them, you might try explaining to your daughter in simple terms how they work, and a comparison to hiccups might be helpful. E.g.(in age appropriate language): Hiccups come whenever they come, they are a bit bothersome, but they're only hiccups. They won't and can't hurt you, and they go away eventually. People can try to stop them (so many remedies -!!!- indicates the desire for control over the possibly uncontrollable) but they always stop, and if you don't dwell on them/if you think about pleasant things, they seem less bothersome. Intrusive thoughts are like hiccups in your imagination: they are bothersome, the more you think about them, the more afraid you are of them, the more you try to control them, the more they seem to control you. But when they come, if you just accept them as a brain hiccup, and know that thoughts are just thoughts, not real, it's just a hiccup, it will become more tolerable and have less of an effect on you.
This video explains intrusive thoughts for adults. I usually don't recommend sites that ultimately peddle a product, but just ignore the end of video product placement. It may be helpful. This video is a child therapist's approach to intrusive thoughts. It's a long video, but the main point is to recognize it's an irrational thought, accept that you have irrational thoughts (everybody does), and move on.
If you or your partner have OCD or ADHD, this may be an indication that your daughter has inherited the predisposition for it. If not, it's still something you might want to discuss with her doctor.
Edited to add: @jpa has a great answer. I wanted to edit to add something which may help, but it isn't a solution, really, as much as an affirmation that might help her through it for the moment, and that is, after showing her the mechanics of how toilets work, have her flush the toilet immediately before sitting, thereby forcing down anything that might come up out of the water. I don't know if it will work; irrational thoughts rarely are conquered by rational solutions.
I'm not suggesting that your daughter has my diagnosis, but I can really empathize with your daughter here, because I had the exact same fear at her age. I never told anyone about it, because I understood it was ridiculous, and I thought my fear would be met with laughter. But it wasn't funny to me. It was only at night, it was very uncomfortable, and I absolutely dreaded going to the bathroom in the middle of the night. It turns out that I have OCD, a fairly mild form of it, and the revelation (by a therapist) that my intrusive thoughts (no longer of toilet monsters) were just OCD provided me immediate relief. I wish I had known that long before I found out.
Tackling Irrational Fears in Children and Teens.