Stated by whom?
Claire didn't start displaying her regeneration abilities until six months before the series picks up. Kensei doesn't just have immortality as he heals from every wound, regardless of whether or not it's fatal. I'm sure if he lost a finger, it'd grow right back. That's regeneration.
I forgot which Hero site quoted Adam being immortal, I will look for that in the meantime.
Yet your forgetting though that it was stated in the first season that they knew about Claires power, Hiros dad was holding her before he gave her over to HRG. Also the event of when Claire met her real mother, the same thing was mentioned on how she was able to survive that fire as a baby.
Yes Kensei does heal himself, its apart of his immortality, yet I still debate that (and I know a few others debate it.) that there are different stipulations between a person with extreme regeneration, and immortality. The only problem with the way they display immortality is his extreme ability to heal quickly, which could either been the primary effect thus leading to his immortality or his immortality was the primary effect and his regeneration is just a secondary effect of immortality.
Immortality is always depicted differently over mediums.
Until proven otherwise, im still going to stay with the fact that Claire and Adam are still different characters with similar abilities.
We've been seeing in this season that alot of people are demonstrating secondary abilities, so this is where the theory about his abilities and claires branches off of, but it has been said that Adam Monroe ability is immortality.
Here is something I pulled off wiki about immortality I thought it was interesting to bring to the convo:
In the film and television series Highlander, once one dies for the first time, if they are an Immortal, they will spend the rest of eternity at that physical age. This poses a problem when one dies as a small child, or as a very old man. The same is true of Kirsten Dunst's character in the film Interview with the Vampire and the Blade television series.