Nearly every list you look at has a different order of "safe" airlines so it is all in the marketing, payola, whatever the criteria are. I doubt if any of them are "accurate".
On the subject of the take off/landing being when the most incidents occur, I am a flying nut (not a pilot, merely a passenger) who thinks the take offs and landings to be the best bits of the flight.
A recent example (and many of you will think I really need help, but I enjoy flying on new - to me - aircraft types and airlines) was a trip from London to Chicago. I could have flown non-stop with BA or AA but I'd flown those airlines before so I ended up flying LHR/AMS/LCY/DUB - overnight stop - DUB/LHR/YYZ/ORD.
It gave me the opportunity to fly Aer Lingus, Air Canada, Air Canada Express, Stobart Air and, as a bonus, a luxury jet from Cello Aviation as the BA aircraft scheduled from AMS/LCY had gone tech. Aircraft types new to me were the 777 and 787 and the ERJ 170 and 175.
The only difficulty I had was the BA check-in person at LHR who couldn't believe anybody would want to fly LHR/AMS etc. Her supervisor was more understanding and helpful.