There was a recent court case that was just settled that probably helped prompt some of this. It was a photo of a bear that fell out of a tree that a student photographer (working for the university paper) got a photo of. It went viral, was used in some Asian add campaign and the student who came on mid-term had not signed a contract. The university paper was trying to collect royalties on the photo. Student sued the paper/university and won the rights to the photo all due to the lack of the contract.
Don't kid yourself, the Paper is part of the university - oversight, budget, etc. maybe separate but they "own" it. Either way it doesn't matter much or make a difference in the situation.
If you want the job sign the contract - there isn't a choice. It is as simple as that. Contracts like that exist with any and every job that is worthwhile. You will gain much more through experience than any single photo you take will ever make you.
What to be sure to do is to get in writing where the Paper's photographs end, and your personal stuff begins. If it is their gear - that is easy, just don't shoot personal stuff with it. If it is your own gear, make sure to log the events and begin and end of the file name sequence and have your editor sign off on it when you deliver the images. That way if some question comes up, it is clear where that line is. It's just like logging mileage on your car to be reimbursed on. It is very doubtful they will let you cherry pick images of an event they sent you too for your own use. If you are somewhere by their request, then it is theirs. If they want to cherry pick from your images, and you get to keep the rest (most ideal for you) then log the file name they are taking. If you have a similar photo (say a 5 frame burst shot of something and they pick what they feel is the best one) you can point to the different file names to show it is a different image. Again, log it & have them sign, or initial what they take. As always, make sure to ask if you can use images for a personal portfolio for future employers as well.
What I have bumped into for the college world series is the NCAA rules for shooting games as part of a Paper/organization with a press pass (not a general ticket holder/spectator) on the court/sidelines are quite strict to protect the athletes. What I understand, the paper can protect you until you start using images for your own use. Some have told me there are some massive teeth that come out if you break their rules and huge fines. Evidently the NCAA is not shy from suing the pants off of photographers who break their rules. It could be that is just something for the CWS, but something to look into. The one photographer I know who has shot for it for 4-5 years now, said she gets a 600+page contract each year to sign. Keep in mind, ignorance is not a defense in court.
Mike points out a great concern about insurance of your gear as well. Today at a FB game I saw a sideline photog get wiped out and his nice shiny white canon bazooka lens was turned into a a movie sequel - Part I and Part II.
I say take the gig, allow them to get you access to experiences you couldn't get otherwise so you can build a portfolio for later. I respect other's opinions not to sign something like that, but many of them are established and have the experience already - something you do not and are much harder to get on your own.