I feel there are multiple notions of "luck" in common use and the ambiguous term leads to misunderstandings.
In my mind, the purest form of luck is, by definition, not something that can be mastered. It is 100% beyond one's control to influence. Examples might include: your genetics, flipping a fair coin, etc.
But lots of people talk about "luck" as though it's something that somehow one take advantage of in a willful way. They say "make your own luck." Or perhaps "put yourself in situations where you're more likely get lucky." Or maybe "master luck"?
That's all fine, and is a worthwhile topic, but I would call that "skill". Maximizing one's odds of something (even something involving luck) is a skill.
Perhaps by "mastering luck" they mean not allowing it to psych you out — even if you're on a long losing streak, even while doing everything right. But again, I'd say saying level-headed is a straightforward skill (difficult though it may be).
Anyway, that's my little rant on the ambiguity of the term "luck" (:
so i think there is a chance that the quoted person would agree with your comment here, as I think it is orthogonal to the quote
Luck follows (or at least positively correlates) with skill :) 30+ years ago in our company of friends in the university dormitories we had a guy who had the card deck handling skills of a major illusionist (and those skills were naturally a source of significant income for him). The guy was also tremendously lucky - well beside mere being alive and without broken bones while applying his skills for income :) - in particular once he won an amount enough to buy 1-bdrm apt in St.Petersburg back then on a scratch lottery ticket that he bought at a random place on our way while we were walking to some business meeting in a city that we just arrived that morning. If it were a skillful illusion, then it was way beyond anything i've heard or seen before :)
Sometimes, you make your own luck...