To nitpick further (but this isn't in common parlance), Accenture was a part of Arthur Andersen, which itself was a part of the Big Five until Enron happened.
But you're entirely right in that Accenture isn't considered a part of the Big Four accounting firms precisely because its skillset is advisory rather than accounting.
To nitpick even further, Accenture was not a part of Arthur Andersen. It was known as Andersen Consulting, and when they split from Arthur Andersen, they adopted Accenture as a name.
"Big 4" used to refer to accounting firms. Accenture used to be a part of the "Big 5" with Andersen, but they had to re-brand because of the Enron scandal. They no longer do accounting.
But now all these companies are bleeding over into each others business areas - many do strategy, operations, implementation, accounting.
another minor nitpick-- Arthur Anderson had just recently spun off its consulting division as Accenture before the Enron scandal hit, not in reaction to it. It was a move that had been planned for some time. And I'm sure they thanked their lucky stars they completed the spin-off before Enron; Accenture was safely insulated from the fallout that absolutely killed Arthur Anderson.
Auditors cannot provide other services—mainly tax and IT—to audit clients for auditor independence (SOX in the US, Combined Code in the UK and similar laws are in application worldwide).
All Big4 firms had to shelve their IT consulting to separate divisions or into new companies which most later sold:
Arthur Anderson formed Anderson Consulting which later became Accenture.
Ernst Young - Ernst & Young Consulting which was acquired by Capgemini
PriceWaterhouceCoopers sold to IBM Global Services