Capita have been known to do dodgy things...
But I'm not so sure in this case. Sounds like a PITA employee who snubbed a 'golden hand-shake'. That's not blackmail, that's an acknowledgement of a breakdown in employee/employer relations.
However in my/our case it was the firing of multiple people on trumped up charges. We were all in the 18.5k pay-band providing tech support on premium rate lines. We were replaced with people paid 13k with less skill = longer premium rate phone calls for Dixon/Currys/PCWorld customers.
In the end it didn't reach the tribunal stage due to a Capita/DSG employee refusing me the right to speak during a disciplinary hearing (thank God I was a Unison member). Two and a half months of back-pay and my choice of Team & Hours is what I got as a result (my new team leader was a genuinely nice bloke too).
It was monumentally hard on me financially & physiologically until the back-pay was provided (@ emergency tax rate). The volume of phones calls and letters to HMRC to properly reverse the P45 so it never happened was also a PITA.
I got out of there as soon as I could afterwards. I fought them because I didn't want a firing on my CV as that would have damaged my career immensely.
She should have just taken the 10k - it's not nice to work somewhere where you know you're clearly not wanted.