Just to be clear, MIT's role was to catch him out by finding his hoovering laptop hidden in the janitor's cupboard and reporting him to cops. JSTOR didn't want to prosecute but the government did, presumably because he helped scuttle SOPA & PIPA and was clearly going to be a powerful thorn in their side in future.
Unfortunately MIT gave the government the excuse they were waiting for to destroy him.
That is what I recall from the documentary anyhow.
iirc, MIT could have denied access to FBI in setting up a trap to whoever was the owner of such laptop. They could've set the trap themselves and dealt with academic discipline too. So, they did enable the up-scalation of the conflict.
Of course, it's all subjective at this point... either I recall incorrectly some details, or even how I unconsciously choose to see it is shaped by personal world views.