Thank you. I saw this as well. Unfortunately this particular IRS publication is rather poorly-written and obfuscates the issue even more for me:
The last sentence in the first paragraph ("whereas any part of such a payment used for the support of the recipient would constitute support of the recipient by a third party") seems to suggest that if a SSI recipient, e.g. my daughter, uses her SSI benefits to provide for her own support, then it constitutes support of my daughter by a third party (i.e. not my daughter providing her own support). But the example in the following paragraph ("If a child receives Social Security benefits, and uses them for the child’s own support, the benefits are considered to be provided by the child") seems to contradict that. Under that example, if my daughter's SSI benefits are being used for her support, then she is considered to be providing her own support.
Maybe I'm reading too much into this and making it more complicated than it is?