So you think that LSI thing is't true ? What if Google has mm Databases Database 1 Database 2 Database 3 and every database gives 1 point for SERP ranking. If your site contains only the keywords you want to target they are connected to database 1. But if you chose also synonyms besides the keywords your targeting they are connected to database 2. So you have now 2 points from google besides 1 point and that makes you rank higher. It's just an example what makes no sense but I just feel that LSI can be true.
I think first you have to know and understand what LSI actually is (try this What is Latent Semantic Indexing?). When you have a grasp of what LSI is your ready for this The LSI Myth. It's a long and sometimes difficult road to understanding but well worth it in the end! Good luck. - Michael