What I mean is, make sure that you've talked to people in the company. Like others have suggested, talk to people outside of the HR department. If you need a suggestion for how to go about contacting them, I've had a lot of success with finding someone who works there, sending them an email with a subject "What's happening at <company name> this summer?" Inside the email, include a sentence about why their company is cool, a sentence about why you'd like to work/intern for them, and then ask them if they might have a place for you.
Not only have emails like this been well received, they give you the chance to craft your initial conversation with a company, and talk to many more companies than going through HR would allow.
In my experience I had a much higher response rate than I expected, and while many weren't looking for anyone, a follow up email asking if they knew anyone who was hiring often produced another lead or two. Best of luck.