There is something in that.
2006, to an extent although I don't think the lasagna thing affected them as much as they make out, they pretty much had a full strength team out. There is always a touch of fortune about relying on another result to go our way though.
I checked 2009 and although Villa did indeed poo themselves they were never that far ahead of us. 5 points at the end of Feb and we finished miles ahead of them and Everton, We won 8 of our last 11, that isn't luck.
2012...suppose so although we were 5 points clear of Spurs before we had a late season wobble so it was us who nearly threw it away on that occasion.
2014. We were 4th with 5 games to go but Everton were only a point behind us and had a game in hand. We won our last 5 games so while we did finish further above Everton than we might have I'd say we earned that one.
2016, we were lucky to finish 2nd but there's very little real difference between 2nd and 3rd, Spurs lost interest when they knew they wouldn't be Champions.

There have been some occasions where we have scraped into the top 4 or had to rely on other results, there are often fine lines in football. Overall though I don't think he has been especially lucky.