First off, congrats on getting offered a position after your internship. That means they like what they see. A lot of new grads aren't getting positions these days, so that's awesome!
Second, if you have the skills to thrive on the web team, you'll have the skills to thrive on the BI team. They're the same skills with a different application of the skills. But problem solving, root cause analysis, and out of the box thinking will be useful on both teams, as well as your technical background.
Assuming you're getting a degree in computer science or software engineering, both of those degrees would allow you to be on either team. So really the work isn't much different.
And most importantly, they believe you can handle it! BI is a bit tougher, and you have to think a bit harder to solve the business problems. They have confidence in you.
Looks like you've got quite the opportunity ahead of you. This is very different than applying for a developer and end up working the phone lines on support all day. It's more of an upgrade than a downgrade (although mostly lateral) so I say take full advantage of it.
Adding this from @Enderland's comment:
I would recommend asking to job shadow some people in that department prior to making your decision. You have a great opportunity to know those people and the work prior to making your decision.