I have been looking over a variety of Hapkido websites. I read things about authenticity, originality, traditionally pure, etc.
How can these claims be verified?
If you look at many TKD school websites, you run into the same sort of thing. Yes, it can be verified, but it takes digging and research. It is much easier to verify with taekwondo than it is with hapkido, partly because traditionally, hapkido has no forms. With taekwondo, you can look at the forms and say, 'he's doing taeguk iljang, or he's doing a Chang Hon or a Songahm form.' Taekwondo is much more accessible to most people, so they also have a better idea of what it is supposed to look like. Since the technical content is generally narrower and more striking focused, it is also easier to evaluate.
Hapkido is less common and really doesn't use forms. It's not an olympic sport and traditionally doesn't have a competitive element, so people don't have a mental image of what 'hapkido fighting' is supposed to look like either. Because hapkido has striking with both the hands/arms and feet/legs, but which are executed differently, and because a lot of TKD schools incorporate kicks from hapkido, it is even harder to differentiate.
Does Hapkido have a technical standard, and if so, what/who sets that standard?
People who don't actually practice hapkido but have material culled from hapkido grafted onto whatever art they practice (usually taekwondo) are happy to say that they practice hapkido (even though they don't) and will say that there is no technical standard. This is not true.
Hapkido, regardless of which federation or association, has a common body of material. There are some differences from federation to federation, but there is far more overlap than difference. Hapkido's techniques are designed around the hwu, won, and yu principles; harmony, circular, and flowing (there is another thread on this subject going). Hapkido is a soft art, which makes it very different from taekwondo or karate.
Aside from joint locks, manipulation, sweeps, and take-downs, hapkido has a body of strikes, some of which overlap with other Korean striking arts and some of which are uniquely hapkido.
As to who sets that standard, it is the same as with any other art; there are a number of federations, the largest of which I believe is GM Ji's; the Korea Hapkido Federation, which set standards for the technical content.
Other organizations include the International Hapkido Federation (GM Myung Jae Nam) and the World Hapkido Association (GM Jung Tae). There are numerous other federations and associations, as well as unaffiliated schools.
I have been trained by IHF lineage instructors and am also a member of the World Hapkido Association.