Why do we think Tuon can channel? When we first meet her in WH, we learn that she has tested to be a sul'dam, obviously successfully, since she "found as much enjoyment in training damane as in training horses" [WH: 14, What a Veil Hides, 325]. (Ick.)
As we know from numerous scenes from TGH on, sul'dam can channel. The difference between them and the damane is that damane are women like Egwene, who are born with the spark, and will channel whether they try to or not, whereas sul'dam are women who can be taught, but would never touch the Source on their own without instruction. So Tuon can be taught to channel - and thanks to Egeanin's revelations in [COT: 29, Something Flickers, 644], now she knows it, too.