They claimed "Monero can be traced", then fumbled when asked for proof

It seems to be they are simplifying the claim a lot, I believe technically it is true.

The only way to trace Monero is to link it to transactions in and out of Monero, which is only possible if someone doesn't allow enough time between purchase and sale, or sells the same/similar amounts of monero that they bought with the dirty coins, all at once. But I think we all knew this already.

@Kodomu yeah this. Timing analysis and coinswap metadata can be used to "trace" Monero. It is more difficult to achieve though because there is no transparent pool and because Monero utilizes many different coinswaps that are nonkyc.
There are known incidents where this has been achieved, but they are rare.

See: https://www.youtube.com/watch?v=ThbSLOVHKVE

@UsualCat
There are so many ways that you can leak data about your transaction to various parties. Even if monero does its job perfectly, you can still get traced if certain information is gathered. Think of it like assembling the triforce from legend of zelda... instead of power, wisdom and courage, they need your ip, the wallet that bought the monero, and where you spent it. Obviously the dealer knows where you spent monero. Obviously the liquidity provider knows what wallet you used to buy it, and probably your ip through tracing that. So if those two parties can get together and cooperate then most users are
DEAD EASY TO TRACE, no doubt.
That being said, Monero clearly works.