Regardless of the immense faults of that study, you're completely ignoring the added need for L-carnitine in people with thalassemia, due to depletion.
I really hate how the media is always so quick to promote bad science or in some cases, no science. The media jumped all over this story, but another study published a few days later gave a totally opposite report about the value of L-carnitine. A study of mice genetically engineered to have heart disease were fed an unnatural diet high in red meat. How does this relate to human beings? Well, we don't know because they ran no controlled study of humans who are not genetically engineered to have heart disease. They looked at 6 humans and then made assumptions. This is not science. There are a host of articles about the value of L-carnitine that show its benefits that are based on studies of humans. The link to the other study is below. I have seen similar hatchet attacks by the media on Vitamin E and vitamin D. I will also mention that being a vegetarian, I never recommend red meat to anyone, and often tell people to minimize their consumption of red meat.
You are free to follow any course you choose.
Here are some commentaries on this "study."
http://jonbarron.org/heart-health/acetyl-l-carnitine-supplements-and-heart-disease#.VxgfMvkrKHshttps://heartmdinstitute.com/diet-nutrition/carnitine-still-good-in-my-book/Here is the study about L-carntine published a few days after the the other study.
https://www.elsevier.com/about/press-releases/research-and-journals/l-carnitine-significantly-improves-patient-outcomes-following-heart-attackL-Carnitine Significantly Improves Patient Outcomes Following Heart Attack