Makes sense to me. We often hear about Aes Sedai freaking out when they're around male weaves, as if they could get tainted just by touching the weaves themselves (which we know isn't true), so it stands to reason they'd assume the Ways could be tainted in a similar way since they were created using Saidin.

The question remains, however, of how Mashadar got into the ways in the first place. Is Mashadar intelligent enough to figure out how to open the Waygate? I don't think so (if I remember correctly, it can only sense food and acts solely on that instinct). Did someone travelling the ways get lost and open the Waygate in Shadar Logoth during the night? Possibly (and that idea or something very like it makes the most sense to me). We've seen, however, that the Black Wind has a very difficult time getting OUT of the ways (the gate itself turns black and boils and churns like a cauldron, but the wind doesn't come out, or not very far). Would Mashadar have the same difficulty getting IN?