I don't think it is lawyer time just yet. Push Jiffy Lube harder and mention that you'll get a lawyer the moment it appears they are being unreasonable. And yes, it is unreasonable to expect you to have the car towed back to their location to have their buddy inspect it. They are a large corporations with locations all over the US. They need to come up with a shop that can do their inspection that is local to you. The moment someone isn't willing to reason with you, ask to speak to their manager or direct report. Until you are speaking to Jiffy Lube President Rick Altizer, there is always someone up higher that is qualified to respond to your request.
I think you have more than a compelling argument that the drain plug fell out. I'm sure this isn't the first or last time Jiffy has forgotten to tighten it while they changed the oil in a jiffy. They will push back so long as it seems they have a chance at you eating the cost. Make it clear that you won't and they'll cooperate.