I know it's small, but the one on our main logo is the same as what I posted in a different color.Yes. In our case, every representation of the spur I've seen on a Gamecock shows it as the attached kind.
Apples and oranges really. Cockfighting is taboo, so highlighting the killing instrument used in cockfighting (as noted in Batgirl's post) would be risky.
I'm not saying I agree with the rationale. Teams should call themselves whatever they want and have whatever logo they want. Maybe PETA wouldn't care at all. They haven't really messed with us for the past 20 years, so perhaps we're just not a big enough fish to worry about.