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.
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.