If you've seen this more then once or twice then I really doubt it's shed intestinal lining and I would treat with a round of Corid. Coccidiosis usually does produce lethargy and puffed up birds but in a situation like this you need to start somewhere and it would be very wise to at least be able to rule out coccidiosis. Older birds who've had a chance to develop some resistance can still come down with it and their bodies may fight it off longer then a young chick would. Better to be safe then sorry. I very, very rarely see shed intestinal lining and it's usually not bright red nor a lot of it.
There is no egg withdrawal period if using Corid (amprolium).
I would treat with Corid (or amprollium, Ampromed, Amprol) for coccidiosis. Blood in stools can also occur with enteritis and capillaria worm, but I don't think it would be that much. Corid is not an antibiotic, so there is no problem eating the eggs. Dosage is 2 tsp of the liquid ?Corid, or 1.5 tsp of the powder per gallon of water for 5-7 days. After treatment (of all birds) give some vitamins and probiotics for several days. If a bird is too sick to drink the medicne, give some with a dropper. Here is some reading: http://www.the-chicken-chick.com/2012/12/coccidiosis-what-backyard-chicken.html