If I find time to research this I will throw some Code Sections at you.. I do know I am correct.

FYI- a 401(k) Plan is a Profit Sharing Plan that allows for elective salary deferrals (this is the IRC 401(k) part). And IRS Publications are not authoritative.

I did a search in the Pub for "catch-up" and every place I found it was referring to salary reduction/deferrals. 

P.S. Your quote from the Pub says "A plan can permit participants who are age 50 or over at the end of the calendar year to make catch-up contributions"   Profit sharing contributions are Employer contributions. Participants make elective deferrals/salary reduction contributions.