"Associated with" means correlation without causation.
If you had looked into this further - as I did when I first learned of it more than a year ago - you would understand that there IS a clear causal link.
Researchers fed participants sugar alcohols - such as xylitol and erythritol - under controlled conditions. They then took blood samples and discovered that the blood of those participants experienced a marked increase in the likelihood of blood clots forming - for up to three days after the last consumption. GoogleAI dug up this Cleveland Clinic quote: "Consuming typical dietary amounts of erythritol or xylitol makes blood platelets—the cells responsible for clotting—more sensitive and prone to overreacting".
IIRC these tests were done to prove or disprove statistical correlation between sugar alcohol consumption and blood clots. Regardless, there is a clear, clinically demonstrated causal link between sugar alcohol consumption and increased clotting; and there is a clear causal link between blood clots and heart attacks. If A increases B, and B causes C, then more of B will result in more instances of C.
As an aside, it seems likely to me that these sweeteners also increase the risk of strokes. That's another reason why I no longer consume them.