They're required to be able to interline since they're a US carrier
First, that's not what interlining means. It refers to whether an airline has arrangements to coordinate with another airline generally, not just in the event of a delay/cancellation/etc.
Second, there is simply no requirement that US carriers make arrangements with another carrier in the event of a delay/cancellation/etc. You may see references to "Rule 240" which was a pre-deregulation tariff requirement, but it hasn't been mandated for decades. JetBlue's contract of carriage voluntarily provides for compensation in the event of "controllable" delays, but makes no provision for rebooking on other airlines.