I think Matthew trained in a Hakuhokai-Takumakai Daito-ryu branch before Okabayashi split off from the Takumakai.
Brian is 100% correct. The period I trained at the Hakuhokai they were still an affiliate of the Takumakai with Okabayashi acting as one of the senior teachers there.
Okabayashi after studying with Takuma Hisa and other Takumakai teachers went on to study with the founder of Daito-ryu's son Tokimune Takeda.
This was problematic for some of the other teachers who wished to maintain the Takumakai's pure tradition. At first there were rumblings when the Takumakai decided to implement the Daitokan's kata for teaching fundamentals into the Takumakai curriculum But it was approved and implemented at that time as they were open to the process of fostering closer ties to the Daitokan tradition preserved by Tokimune. Later when Tokimune had passed away and Okabayashi wished to implement further changes in the curriculum in accordance with what he had learned from the Headmaster it seemed appropriate for him to separate rather than asking others in the association to accomodate him.
This however happened a year or two after I left Japan.
As for the seniors at the hakuhokai they seemed to believe that there were striking similarities in many techniques I showed them from hapkido as well as some clear differences.
I think that this may be a function of hapkido being a composite tradition with Daito-ryu only providing one of the influences that went into the composition of the art.
Still that there is some connection seems obvious. Most techniques found in hapkido exist in similar forms in Daito-ryu. Some things which are obvious artistic/aesthetic things rather than purely functional things are held in common between the arts. Some of those techniques held in common are techniques which not present in modern aikido.
On the other hand Daito-ryu and hapkido move in different ways (as is also true of aikido) prefer different stances and 'feel' different. There is definitely a disconnect there as well.
Not all traditions of hapkido are the same however the one I practise definitely employs internal practise. Perhaps more so that Daito-ryu. anyway, certainly as much.
Perhaps atypically, I don't necessarily equate 'aiki' with 'internal practise'. 'Aiki' is coordinating movement and intention in combination with and one's opponent's movement and intention. I think of internal practise as coordinating one's breath and a relaxed movement in such a way as to create power. One can often see 'aiki', whereas internal practise happens specifically within for a variety of purposes.
One could have an 'aiki' situation without having done any internal practise and one could do internal practise with manifesting it into aiki.
I also think "Ki" in Japanese is used much more prosaically for energy or spirit than most North Americans presume.
I've also had high ranking Daito-ryu practitioners describe which part of the hapkido techniques I am performing on them as the 'aiki' section of my technique... so I guess they must have thought hapkido had some.
Still hapkido is more direct and less subtle than Daito-ryu generally and often does prefer jujutsu techniques which damage to aiki tactics which unbalance. I never felt that this was a bad thing although I appreciate the beauty and depth of Daito-ryu.