My wife had the same experience during our green card process when she was on an EAD and a company said they couldn't proceed until she got her green card. Now, I don't think it was on purpose. The person she was talking to was young and, while most Americans know what a green card is, probably very few know what EAD is so they'll just default to the safe answer.
Your wife should probably answer with "I have legal work authorization in the US" and leave it at that. Really, this is what the recruiters should be asking as well, not whether or not she has a green card.
My wife had the same experience during our green card process when she was on an EAD and a company said they couldn't proceed until she got her green card. Now, I don't think it was on purpose. The person she was talking to was young and, while most Americans know what a green card is, probably very few know what EAD is so they'll just default to the safe answer.
Your wife should probably answer with "I have legal work authorization in the US" and leave it at that. Really, this is what the recruiters should be asking as well, not whether or not she has a green card.