Yes, I did see the cause of death. Very tragic.
Ethel is down on the censuses as clearly born in England and having arrived in 1905. One would think the Brooke adoptive (?) parents would have known that. An Ontario birth cert would be available if she was born there.
Online trees are notorious for having errors, unfortunately. I'll have a look at trees later. I do think she is your Ethel Noakes. Difficult to prove outright, though unless you can find a connection between her and her brothers or their descendents who knew what happened to her. As you mentioned earlier...accepting her but with a notation.
PB