Stats such as these can be misleading, especially the "winrate when played." Prince Liam is usually played when you already have the setup for a lot of legendaries, so in general you may already be ahead and more likely to win, thus inflating the winrate. The Soularium suffers the opposite problem since you play it when you're most likely behind, deflating the winrate.
Hsreplay winrates =/= actual winrates. They're heavily influenced by which popular streamers play them, and more importantly, by how good that audience is. For example, if the world's greatest HS player spent 500 games running Even Shaman with Boulderfist Ogre, he could probably pull off a 60% WR, even though they deck is obviously not optimal.
That said, I did take Liam Odd Paladin into the Brawlesium, and I got 10 wins, and while he wasn't great, he also wasn't bad.
Also, only a fool would say that Prince Liam is better than Baku in Odd Paladin. Baku's played WR is low, but that obviously doesn't matter.