I'm not sure what traits she'd have that would tie her to Fate and Yuuno. Because she has one eye of each of their colors? In StrikerS, she deliberately watched and copied Nanoha and Fate's spells, so she would be using those in combat, which would lend more credence to her being Nanoha and Fate's child.
Anyway, I'd just chalk it up to people's abilities to see connections where there are none. We do it all the time in real life, and it leads to weird things like conspiracy theories. "Hoki and Old Iron posted in the SAME thread! They must be the SAME person!" It's faulty reasoning, but we humans are so good at it.
Now, on the other track, my own "reasoning" is that Vivio was meant to be Nanoha and Yuuno's child. Yuuno having good defensive abilities, and Nanoha having good offensive abilities, pair those in a child... Vivio has really good defense and offense, at least in StrikerS. Which makes me think that Tsuzuki initially had the idea for her as a possible child, given that he initially planned on Nanoha/Yuuno. But after seeing the insanity of Fate fans, he decided to make her adopted instead, and retooled the story.