Great lesson!
And you are correct--you cannot impart it upon your pwBPD. Any more than you can actually fix her unhappy feelings.
The best you can do is make it clear to her (either with words or actions) that you are not actually going to take responsibility for her feelings and try to fix them.
And since her "requests" and your attempts to manage her feelings were mostly done through indirectly stated undercurrents rather than direct words, your (new) response will be similar much of the time.
One magical thing about proper validation is that it often puts the responsibility EXACTLY where it belongs... .in effect, you are acknowledging her feelings, and handing them right back to her. (Instead of trying to take away her 'bad' feelings or give her 'good' feelings!)
You can also care for her, and you can do nice/kind things for her still... .and let her choose her feelings in response. (As if you could do otherwise... .)