Here's my 2 cents. Pigs is right. Especially with the chicken thing...wow.
The guts of the problem is juices spent in the temp zone of 40* to 140* for an extended time. The cross contamination (this is in my opinion) is where work is done on a cutting board (elapsed time here), then without cleaning, go onto another meat. This means the first meat's juice has now spent extended time in the temp danger zone and bad things develop. Beef mixing with chicken does not produce anything nasty. It's time vs temp.
Chickens have more bacteria to start with and need more care with the danger temp zone.
I'll shut up now.