During one raid on Lille in Oct 42, B-17 gunners claimed 56 destroyed, 26 probables, 20 damaged. Post war analysis of German fighter losses indicates probably 1 Luftwaffe fighter lost.
On the first Schweinfurt raid, US bomber gunners claimed 148 enemy fighters shot down, 18 probably shot down. The escort fighters claimed claimed 19 kills. Actual German losses 25. The fighter kill claims were on average twice real kills, so around 10 fighters shot down by the escorts, 15 by the bombers.
These are just a couple of examples, but it's easy to see why bomber claims were so inflated. Any fighter attacking a bombing formation is going to have many guns shooting at him at the same time. If the fighter is destroyed, all those gunners will file a kill claim.
I've seen the figure of around 1000 fighters as an estimate of the numbers shot down by USAAF heavy bombers over Europe, which includes the B24 as well. To put that in context, That's about the same number the 109 or Hurricane claimed in the BoB alone.