If the doctors did this without her knowledge/consent, it was/is unarguably wrong.
But.....
The 'right' to have children comes with responsibilities. Too many consider their rights, including that of procreation, to be absolute and unfettered, while failing to acknowledge and live up to the responsibilities those rights entail.
This woman should not be castigated for being on welfare, nor does she deserve hate mail.
In this day and age, far too many of us are dealing with (or on the brink of) real financial hardship, and will be grateful for any safety net afforded us. We should be a caring and compassionate society that helps those unable to provide for themselves.
That said, I feel it is irresponsible (socially, economically, and ecologically) for someone who cannot provide for herself and must live on welfare to continue to choose to have children.
Having a child is (at least) an 18 year commitment to provide love, shelter, food, clothes, nurturing, education, etc. Her expectation that society will step up and assume the task she is unable to complete on her own is wrong. She is not entitled to continue having children she cannot provide for.
Her right to procreate should not require society as a whole to assume financial responsibility for her children. Is that the law? No. It's a question of fairness and doing the right thing.
But to go back to the story that has prompted the debate: as stated earlier, something doesn't add up. I doubt two doctors got together and hatched a scheme to secretly sterilize this woman. They must have at least thought they had permission from her.