Is Monero double-spent proof?

Short answer: no.

Long answer: This is a misconception coming from the CryptoNote whitepaper's use of the term. What they mean is that CN coins are double-spending proof under normal conditions (i.e. no one has >50% of the network). This would not be worth mentioning for normal signatures (BTC-derived coins) but special care had to be taken to make ring signatures double-spending proof. However, it's still vulnerable to the standard 51% attack like any PoW system because that allows replacing key image sets.