Which various parts of the world? The only I know of were in North America.
There really isnt anything that suggests Switch was over shipped last quarter, the shipped vs sold difference at the end of 2018 was lower than PS4 in 2016, 2017 & about the same as 2018.
Your last paragraph is a contradiction, you wont count predictions/rumors for Switch but will gladly accept them for PS4 because a price cut for PS4 is nothing more than a prediction. You cant accept them for one console but disregard them for another when trying to make an unbiased analysis.
I will give up my first point on deals because despite remember reading there was deals for Switch in various places in the west during Jan and Feb i am too lazy to search in the internet to prove my point. So let's say i was not right on this.
I wasn't trying to say Switch was overshipped. It was correctly shipped due to time and circunstances. Every console that is very succesful in Q3 has around 2-3M left in stock. It happened to every other succesful console and it happens in other markets with other procuts too. When you had so much stock left, you have to sell it and it's very common that companies use very good deals during some points in the year to sell that stock. I just think that Nintendo to reach their goal for FY, they used those deals (that i can't prove anyway because i am lazy) and that's is why Switch sold so good during Jan and Feb. But that's just my impression, nothing more.
As for the last point. It was not a contradiction. What i meant to say is....that if i was in charge of Nintendo and Sony, i will not make a price cut for Switch because it'ss selling according to plan and even better than expected but i'll do it for PS4 because i think the sales are going to be lower than desired. Neither decision is based in rumors about future, i am just reading the sales numbers right now and anticipating what's going to happen.