There is nothing wrong with HR having that information. It's only illegal to base hiring/firing decisions on protected information, it's not illegal to have it.
Obviously it gets really tricky to prove someone did or did not use protected information in their hiring/firing decision, so it's clearly safest for HR to avoid having any of that.
Why would a resource department need information from payroll? They aren't the bosses of the employees so it's not like they are making the ultimate hiring decisions.
In your company that may be the case. Some (many, especially public) companies use HR as the initial resume filter. They are supposed to make sure the resume is accurate, the applicant didn't lie about job titles, dates of employment, education, etc, and sometimes the dreaded keyword scanning. Some places they'll also do the initial phone screen to make sure the applicant can form more-or-less coherent sentences. Then they give the person hiring a stack of screened resumes, and that person then does the interviews for the actual position in question.
And I have worked at places where HR could unilaterally veto a given employee based on certain criteria (education, background check, etc).
Obviously it gets really tricky to prove someone did or did not use protected information in their hiring/firing decision, so it's clearly safest for HR to avoid having any of that.