Can lowering fill factor result in more page splits?
When you have lots of page splits caused by random middle-of-BTree inserts, your pages will naturally average around 65%* full.  Split pages start at 50% full and any that fill up past 100% get split back down to 50%.  

So rebuilding your index with a fill factor of 85% might temporarily increase page splits, just not as much as rebuilding with a fill factor of 100%

*Why not 75%?  I think it's because each split page covers half the value range of the original page, the new pages fill up half as fast as the original page.