You're right. Although at least two-thirds of the US BoN team are SCA guys.
It seems to me that those guys at the temple are fighting each others' swords, not each others' bodies. There's a pretty significant difference, as demonstrated by the clip I posted in response - I'm pretty sure those Sikh are trying to drive each other away, and not hurt each other.
And the Sikh swords are almost certainly "real" but with rounded edges, like the BoN ones, which have an edge profile shaped like the curve of a euro coin, or a US nickel. Still demonstrably capable of chopping off fingers, and thus meeting the requirement of baptised Sikhs to always be armed, but much safer for flailing around with in a crowd.