Yes, of course, they’ve gotta have the skills! But…I’m frequently amazed at interview situations where nobody probes for the actual skills required by the job. It’s easy to get swayed by very friendly or very persuasive personalities, but at the end of the day you need skills. Test for those specific skills! Give them real situations and see what they’d do.
But just remember: if they’re a little shy on skills but are strong on the other three criteria, the chances are good that they can develop the specific skills on the job.
You’ve hired people and built teams. Does this ring true? If so, I’d recommend structuring interviews and hiring/promotion situations along these lines. You’ll be glad you did!