Your original thinking is correct.
The person in the video doesn't know what they are talking about. 다니에라 would be [Daniera] with an "r".
The ㄹ pronunciation goes like this.
1. between two vowels -> like r. 마리 [mari], 이르다 [iruda], 알아 [ara], 모리스 (Maurice).
2. before a consonant or at the end of a phrase -> like l. 밀다 [milda], 알더스 헉슬리(Aldous Huxley), 앨리스 (Alice),
(it becomes two ㄹ's when the next sound is a vowel.)
3. In the beginning of a phrase -> l or r (it varies). Some people pronounce 라디오(radio) with an r, and others with l.
(This is partly because most words starting with ㄹ are from foreign languages.)
So one or two l's between vowels in Western languages usually becomes two ㄹ's.
- Galileo = 갈릴레오.
- Elias = 엘리아스.
- Gulliver's Travel = 걸리버 여행기.
- Daniella = 다니엘라.
- Delilah = 델릴라 (or 딜라일라 in English way). Sometimes people say 데릴라 because it's easier, but it is not the right pronunciation.