Housing Benefits for wife of Economically self-sufficient

Hi. I'm from Denmark, and on a disability pension from there. My wife is from the US. We have been living in the UK since January 2013, and just got her EEA2 Residence Card back in October. She is looking for work, but so far no luck. I was wondering if we could apply for Housing/Council Tax Benefits without it affecting her right to stay here and her possibility to apply for ILR/British Citizenship after 5 years? We could really use just a little bit of extra income right now, but of course not at the expense of her immigration status.

Thank you very much

PS. I called my local Civic Centre to ask about her right to receive benefits, and they said that if she has a National Insurance number, she can. Which she does, and has had since March 2013. I'm still worried that it could affect her immigration status if we do apply for it, so my question still stands.