Are they non-standard, or invalid (until if/when SegWit is activated)?
Today they are valid and non-standard.
IIRC, amaclin had claimed to get BC.I to display a SegWit transaction that was
"from" an address whose private key he did not control/have possession of.
true.
So why does BC.I accept this transaction while almost all other
nodes reject it? Are they running an older/newer node or something?
Because the policy VERIFY_CLEAN_STACK is not set on bc.i
Blockchain.info is likely running a node version that understands SegWit.
Other blockexplorer nodes are likely running older non-SegWit versions.
Wrong