He didn't realise, and nor did I, that they only stop with military modernisation. Nowhere is it stated in the game that this is the ONLY way. In all other event chains such as peasant wars, religious strife etc, the goal is to get to +3 stability and wait for an event to disable the harmful, damaging modifier.
In this case, I didn't want to modernise my military right away since it was 1520 and my Byzantine units were still better than the medieval latin ones for a while. But I had to go and read the wiki and the forums to work out that you need military modernisation to remove the malus. It's not actually said anywhere, and that's because the military decision is a later bolt on.
Now, when you look at military modernisation it says 'Western Influences is removed', but that doesn't mean it couldn't be removed from other means. What the events and the game needs is clarity here!