Here's a pic from a crashed Jug that had an oil leak. It could well have been what brought it down. I offer it FWIW as it's obviously not the last word on this
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This pic is from page 353 of William Wolf's
American Fighter-Bombers in World War II: USAAF Jabos in the MTO and ETO.
There are several things to note here...
1. The Jug's oil tank contained 28.6 gallons and was mounted on the firewall at top center, not far in front of the cockpit. There does not appear to be anywhere near 28.6 gallons of oil, nor even much evidence of oil at all, visible on the plane.
2. The oil on the tail is dark but not opaque. Note that you can still read the serial number through it.
3. The oil on the tail seems to have come from flying droplets in the airstream rather than from running along the fuselage. Note that there is no big oil streak down the fuselage side. Also note that guys are leaning on the fuselage side up forward, which I doubt they'd do if it was a big, oily mess.
4. The droplets hit the only frontal area of the tail, it's leading edges. From there it streaked, but not that far, only about 1/2 way from the leading edge to the control surface hinges. But this is in the boundary layer where airspeeds are low, so is probably not representative of something angled right into the oil flow, like the windshield.
5. Unfortunately, you can't see the windshield. You can, however, see the bubble canopy. It's not too clear--you can't see the guy on the left wing through it--but it's hard to tell if that's from oil or just sun glare. Note the angle of the shadow of the tail, which seems to indicate that the canopy is reflecting right back at the camera.
6. There's something dark on the upper left wing that's not on the upper right wing. However, I think that's just dirt because it's so far outboard. I figure the plane bellied in from the left side of the photo and dragged the left wing at some point, which spun it around and plowed up dirt which landed on the left wing.
7. I think the pilot's still in there. The canopy's still closed and the red cross jeeps are still there.
8. No telling what the left side of the fuselage looks like. However, even if oil streaked all over it (which might be why everybody's on the right side), it didn't reach the trailing edge of the tail.
