The odd thing with Betsy's response is she seems to think (or have thought beforehand) that Lance's entire purpose of doing this was to make amends to her.
Several times she said things along the lines of "He owes me that".
Here's the thing... confessions of any kind are almost NEVER about the wronged party. They're generally always about the ego of the person confessing. This isn't a "Lance" thing... it's the nature of confessions. They're always focused on the person confessing, not who they may have harmed.
And even so... in the grand scheme of things, Betsy isn't that important. Lance said horrible things about her, but that's really a sidebar on the main story to everyone except her and Frankie.
Lance's purpose was either to cover his **** or to make his concience feel better (or perhaps some combination of both). By not denying or admitting to what Betsy has claimed, he's clearly wanting to cover his **** from a legal angle on that score (not contradicting anything he's said under oath in the past), and he's not remorseful enough about that particular incident to overcome that, especially as he (and frankly most other people who's opinion he's trying to influence) really don't care about that whole incident. If you admit to doping, does it matter to most people if you confirm a specific incident where someone claims you admitted to doping before (other then to Betsy)?