Tetrapod Zoology writes about the mysterious babirusa:
Despite the ancient divergence of babyrousines from other suids, a male babirusa hybridised with a female domestic pig at Copenhagen Zoo in 2006. Of the five resulting piglets, one died but the others survived. As you can see from the photo here, they look surprisingly normal.
Timeframe of divergence not entirely clear; certainly Miocene and possibly Early Miocene. Babirusas are number 2 on my list of why we won’t find hobbits on Sulawesi.