Don't let those professors, who probably have never ventured into the real world of work, dampen your spirits. While "many" have offered a negative opinion, obviously some have provided positive guidance and encouragement. Build on this input and follow your instincts.
As I stated, my "entry-level" position was as a Personnel Assistant - working with the Benefit Administrator I came to know, in-depth, the various nuances of the Health Care industry. (Today, in the US, it is a hot topic due to rising costs and employers' cost-shifting strategies); Safety, including OSHA, as well as Worker Compensation, and Accident Investigation; Recruitment, Selection, and Orientation.
Never did Payroll, each Company I worked for had a separate Payroll Department, or outsourced it.
You have taken the first step to "get into the locker room" by looking into HR internships. Although not with "big corporations", exposure and how you approach the opportunity could be beneficial in the future.
Consider: "Do you want to be a small fish in a big pond, or a big fish in a small pond?" "Big corporations" don't offer the job security they once did. More challenges and growth potential are found in small, "start-up" companies who have the flexibility to respond quickly to market changes.
Should the internship not come through, search the web for entry-level HR positions. Browse websites, such as Monster.com, Yahoo.com, and the local Chapter of the Society for Human Resource Management (SHRM). In addition, your College placement office, and the local employment service may be of service.