I do a lot of radiocarbon dating so maybe I can take a whack at this.
A fresh cadaver would be heavily contaminated with post-atomic bomb carbon, and would not likely provide a reliable date. Further, extremely young dates are problematical because of the ± factor. Even if you have a very good range, say ±40 years, when you calibrate your date at two sigmas you have a range of about 80 years on either side of the intercept (center). So you could potentially get a calibrated date at two sigmas of AD 1860-2020. That's not of much use in determining if a cadaver was from WWI or WWII.
A fallen log could have quite an age range. Take either a redwood tree or a bristlecone pine from the White Mountains of southern California. Each could have wood going back from several to many thousand of years old. Archaeologists take these possibilities into account when dating charcoal.
Hope this helps.
Carbon Dating? Gross!