Jill's picnic is the last opportunity she has to spend a lot of time with MC. She's finally got the all-clear from Bella that he's a good guy but Tybalt has tied a leash to her and she knows that she has just one final chance to sneak away with MC to explain why she can't see him even though she is interested. During that picnic she gets to post the Rooter pic and get the affirming comments from her friends, plus she gets to share positive time and experiences with MC. She gets to see his vulnerable side with the horse encounter and they have goofy fun (which we know Jill loves) in the rain. It's a wonderful second date and they get comfortable together, so much so that she's willing to use her precious film cartridges so they both can have a memory of the date. Without that photo she doesn't have the constant reminder that he is available to her, and she doesn't have his face in front of her to masturbate to. Those are powerful reminders of MC that keep her going and maintain her interest. If they don't go on the picnic she doesn't hear MC vow to see her no matter what Tybalt does, and despite her protests he exhibits an alpha male attitude defending their right to see each other that probably gets her primal juices going.
It's also important to remember that Sage and Jill don't have a positive relationship. Sage has treated Jill badly for no discernable reason whenever Jill made an overture to her, so MC choosing Sage over her probably tells Jill that MC may not be her kind of guy after all. Jill doesn't trust herself at all, and her negative self-talk would lead her to abandon MC if she thinks he's not the right one for her.