Just to clarify, this isn't universally accepted.
It is universally accepted, by hapkido practitioners. I can't speak for non-hapkido practitioners, such as yourself.
The source for such claims seems to be Choi himself,
I choose to believe GM Choi, since he really has no reason to lie about it.
However, the records of the Daito Ryu show no record of Choi's name,
First of all, all of TAKEDA Sokaku's records (which were payment records) are still with us today. Some were lost. But since we are on the topic, do the records show Tokimune Sensei's of the dates of his participation at seminars? If so, how much did he pay his father for lessons?
there is no corroborating evidence of Choi living with Takeda, let alone being an "adopted son"
GM Choi never said he was adopted by Takeda Sensei; what he said was he was with Takeda Sensei for so long that he felt like his adopted son, that Takeda Sensei was like a father to him. Many people say similar things, without the legal paperwork being done. One of my instructors and I are very close, so much so that he once told me that I was like his younger brother. But according to you, this can't be true, since there is no "record" or "corroborating evidence" of this.
Ueshiba Kisshomaru, son of Ueshiba Morihei, founder of Aikido, has said that his father (Ueshiba Morihei) mentioned a young Korean person, aged about 17 or 18, who attended one or two seminars of Daito Ryu, and when training, treated Ueshiba as the senior (which would not be the case for an "adopted son" who trained as long as Choi claimed to). Kisshomaru went on to say that the young Korean continued to keep contact with Ueshiba Morihei for a while afterwards as well, which presumably included the two training together on occasion.
What Kisshomaru Sensei said was his father told him that a group of Korean students took a seminar with his father, and that after his father passed away, Kisshomaru Sensei stated that he received a letter from GM Choi. What I would like to know is what was written in the letter that GM Choi sent to Kisshomaru Sensei. That would be revealing.
I personally find it more likely that Choi had a little exposure to Daito Ryu (through one or two seminars, not formal training, and certainly not long term training), and then continued to have contact with Ueshiba, to the point where he realistically was actually more training in early Aikido (which was closer to Daito Ryu in application, anyway), and then wanted to introduce, or create, a Korean form of Aikido.
So are you now saying that GM Choi did study with Takeda Sensei? I thought you said that wasn't universally accepted?
The problem with your conclusions (outside of the fact that you misstate what Kisshomaru Sensei actually said) is that Morihei Sensei wasn't there 24/7 with Takeda Sensei, so he wouldn't know the extent to which GM Choi was or wasn't there. Just because he mentioned a seminar in which Korean students participated doesn't necessarily lead to the conclusion that that was all GM Choi did.
Another problem is that from the very beginning, GM Choi referred to his art as Dae Dong Ryu Hapki Yusul (Daito Ryu Aikijujutsu in Korean), which was later changed to Yukwonsul, then to Kido and then finally to Hapkido, only after his student GM JI Han Jae printed dan certificates for him to issue with the Hapkido name on it. If anything, GM Choi went out of his way to NOT use the Hapkido name, until the mid 60's or late 60's, which is twenty years after he returned to Korea.
There are some rather large gaps between the approach of Daito Ryu and Hapkido, the lack of formal kata taught in a progressive fashion, instead having a range of techniques that are then taught as separate components, put together at the practitioners discretion, which, again, is closer to the way Aikido was trained under Ueshiba Morihei (it was Kisshomaru who re-organized Aikido in the AikiKai in order to give it structure and a form of progression, but still not the classical kata form expected of a Daito Ryu approach).
I find it interesting that you also see a difference between Hapkido and Daito Ryu. To some people out there, it's all the same. Let me ask you, do you see a difference between Hapkido and Chin Na or a difference between Daito Ryu and Chin Na?
So Daito Ryu? Yeah, to a degree. But more realistically, only in a removed way. Early Aikido is where you should be looking.
Even assuming you are correct, then the conclusion would be that GM Choi did learn from Takeda Sensei, which what you quoted from my prior post and you said was not universally accepted. You accept the fact that GM Choi learned from Takeda Sensei, right?
In concluding, I find it fascinating how on one hand, Japanese style martial artists are quick to state long and loud that Taekwondo is "nothing more than Shotokan", even though there is no corroborating evidence or documentation to that effect. But when it comes to Hapkido, those same practitioners will argue there is no connection between Daito Ryu and Hapkido.