Thank you for sharing this! However, I believe that it is correct.

• If two vectors are uncorrelated, then they are orthogonal to one another.
• If two vectors are orthogonal to one another, this is a special case of being linearly independent of one another.

Source: https://rstudio-pubs-static.s3.amazonaws.com/474212_25a7bbd5f7394f0bae24391cb9587962.html

I would be happy to edit “independence” to be “linear independence.” However, if you have a reputable source that confirms your statement, I’d definitely consider editing it further!