As developers who have released full length games for free - and announced and advertised as such - that paucity of price aspect alone does not guarantee a higher download rate. Connection with the content does indeed appear to come first.
More than enough free stuff available. Genuine free stuff, pay what you want, free with in-app purchases, and so on.
Plus, many players have a huge library of unplayed paid games from all the sales.
So, yeah, "connection with the content" is a must. If you are established as a developer, that one gets easier.