Ages ago, when I started work, all new grads from “regular” schools got x. Those from the little Ivies (almost exclusively NESCAC given that recruiting was all in person) got x+5%. Ivies were x +10%. Because x was so low (ages ago), the real differential in $ was also quite low, and usually, at the end of the first 1-2 years, this had been entirely overridden by performance.
As to OP’s question, I have not experienced an offer being rescinded but as an employer, everyone grumbles when new grads (many converting from interns) try to negotiate offers. The company has a pay scale for that level and often, the decision about who should get offers has had its own challenges internally. If it’s truly not enough and you’ll have to turn it down, sure, it’s fair to ask.
Otoh, it’s totally okay to ask when they’ll have their first salary review, what career progression looks like, etc. Overall, unless the offer is way off, I don’t think presenting info on market rates is generally well-perceived. Having another competitive offer is far more compelling, AND you run the risk of being told “take it.”
Someone with some experience can definitely negotiate.
And yes, as @blossom wisely counsels, do this with tact and grace. And if there is something that would be particularly helpful – more relocation, an extra week in a hotel, – that’s often easier to accommodate than a higher salary. Be sure to express gratitude for any consideration given to the matter regardless of outcome.