It is meant as an expression of gratitude, not absolute fact. There is no way to know if someone could have accomplished the same goals without the support of their parents. It is only possible to know that things the parents did helped immensely, and that the benefit was felt and savored.
There are people who succeed with no help or support from their parents; sometimes it is the lack of help and support that actually drives the need to succeed. It depends on the unique personality of the person involved.
In an ideal world, every child feels supported and loved, so that they grow up feeling they couldn't have done half of what they've done if it hadn't been for their parents. But this isn't an ideal world. You take the lot you've been given and do the best with it that you can.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).