Um, no. Jobs was ousted in the mid-'80s. He was not the CEO of Apple -- that was first Mike Marrkula, the venture capitalist Jobs and Wozniak brought in to help launch Apple, followed by a decade of John Sculley, then a brief tenure by Michael Spindler before they brought in Amelio from Intel. Jobs was never CEO before 1997.
Amelio's brief was, indeed, to "get their product strategy back on track," but it was not, as you make it sound, to straighten out a mess left by Jobs. During those years, Apple coasted on the Mac's momentum from the '80s, making incremental improvements as one next-generation OS project after another floundered. Amelio bought out Jobs' NeXT, whose Unix-based OS grew into OS X.
The Jobs effect can be summed up in one word: Vision. From the time Hobs left until he came back, Apple had none. They tried to out-commodity Wintel with a series of lackluster beige boxes and licensed clones. Apple without Jobs had only one innovation: The Newton, which was in many ways ahead of its time, but never really came together.
Gil couldn’t manage the engineers because they were all a bunch of whiners. They wanted Jobs back.
By 1997, there were few engineers who'd ever worked with Jobs. Any who were that adamant about working with Jobs would have gone to NeXT, which was making seriously innovative boxes; though they were never commercially successful, there was one around for Tim Berners-Lee to invent the World Wide Web on.
It may well be the case that Steve Jobs is an egomaniacal jerk. I don't care; I'm not looking for a carpool partner. What I am looking for is constantly improving technology from a company that has the vision to create it and the financial strength to bring it to market, and on that Jobs has delivered in spades.
And the main reason was -- you guessed it -- a lack of vision by Sculley, the man who pushed the project. They didn't really know what they wanted in the Newton when they started the project back in the 80s. It flip-flopped around for years, changing scope, purpose and form factor.
Probably the smartest thing Apple did during Jobs' absence was to hire Jonathan Ive. He did some good design work before Jobs, such as the Newton. But it's Jobs who recognized his talent and gave him the resources and freedom to really shine.