Unless you're listed as a director or co-owner, her tax bill is not your problem.
However, where she may be able to obtain money from you is the three years you lived as common law husband and wife. She could argue assets outside the business are joint property and this may also apply to debts.
If she makes this claim, you might have to pay a portion of her personal debts as a common law debt. However, I would seek legal advice on this and not rely on the advice of random people on an internet forum.
I would look also at the amount she's claiming and compare with legal costs contesting her claim. You might have the legal arguments on your side, but legal costs may outweigh the claim she's making and it might be cheaper to write her a cheque to settle.
Personally I wouldn't bother with this unless she brings a legal claim to him. Given she has a hefty tax bill to pay it's unlikely she will look at putting herself in more debt to try and pursue what looks a very dodgy claim. The onus is on her to legally show he is responsible for half this bill. From what he has said she cant. It was never his or their business and they were never married therefore he has nothing to worry about imo.
The most I would do OP is maybe briefly speak with a solicitor, one that does a free 30 min consultation. I certainly wouldn't incur any costs or consider paying towards any of that bill.