Well, maybe your friend could now find greater success with this guide in the current season x)

As for your question, I usually take blue smite because movement=kill pressure and agency, but sometimes its just not worth taking it over green due to its CC reduction. There are many cases in which blue smite just lets you stomp over the enemy, where green would just not provide anything for you. It has a somewhat decent synergy with the E, like when you need to quickly chase someone on low HP, this works best especially if you use ignite, since you have nimbus cloak. But I prefer to hold onto my E if its possible, which is why the movement speed from blue smite is very good, since I get to run towards the enemy without wasting my E and snapping back before I want to.

As I already mentioned, the most crucial thing to make Yone Jungle viable is movement, which basically means that if you pick Yone into a CC heavy comp you're already in a losing position regardless of what you do. In moments like these you take green smite to increase your chances of success. You're not gonna get much use of movement speed when you cant move regardless afterall.