Many EEs come from breeding Easter Eggers to each other, not from crossing purebred Ameraucana to anything. So any crosses to Ameraucana or other breeds may have been many years ago.
Yes, she does look a bit like the jungle fowl hen, and likely has a lot of the same genes causing that appearance. Welsummers and Brown Leghorns often look similar as well.
Among purebred Ameraucanas in the USA, one variety is called "Silver," and has most of the same genes as well. The difference is just in whether it's got the Silver gene or the gold gene. (The gold/silver genes are responsible for a number chicken varieties that come in two colors, like Gold Laced and Silver Laced or Columbian and Buff Columbian.) I don't know why the American Poultry Association recognizes Silver Ameraucanas but not a matching gold version, but genetically it's simple to start with Silvers, introduce the gold gene from any other chicken that has it, and ultimately develop a flock that mostly look like your hen.
(I'm in the USA, and Ameraucanas were originally developed in the USA. If you are in another country, different varieties might be available there.)