I don't think that was his motivation. McCain-Feingold was older than his presidential run. McCain doesn't like to think of himself as having flaws. Hence, his getting caught in the Keating 5 isn't a flaw on his part, it's a flaw in the system.
This was not in reference to McCain-Feingold.
From the article:
"McCain sponsored legislation last Congress that included an even broader requirement for grassroots lobbying coalitions to reveal their financial donors."
I suggest you look back on the Republican Primary debates from 2000.
On January 7, 2000, in a debate in South Carolina, candidates were asked to name their biggest mistake made as an adult and what they learned from it.
Orrin Hatch said he had made so many he couldn't name one.
Gary Bauer refused to discuss any personal mistakes.
Steve Forbes referred to editorials he had written calling for positions such as raising gas taxes.
Alan Keyes said that was between him and his priest.
George W. Bush said it was trading Sammy Sosa to the Cubs
John McCain said it was his involvement in the Keating 5 scandal, and said it "will always be a mark on my record and something that people will judge me for the rest of my life."
It's rather interesting the number of candidates, including Bush, who weaseled their way around that question.