Right. Your wife is thinking of the next step up from the 暂住证, the 居住证. The temporary residence permit is, as frb said, for everyone. My husband has had one since we first moved to BJ in 2008. We only ran into the tax issue this year, when we moved to Shijingshan district, but our landlord paid it when we asked, but we have an awesome landlord. When we lived in Haidian we never were asked to pay any tax and getting my husband's 暂住证 was really really simple.
The second one, which requires residence for two years and steady employment where your employer will vouch for your need to be in BJ (so, no nongmingong don't count), is what will allow your kids to go to school in Beijing. That said, even though your kids can go to school here with the jvzhuzheng, they will have to go back to the hukou province for zhong and gaokao. So it is still kind of a crock.
Interstingly, this year the guy at the PSB who fleeced our landlord for the tax money (this is not a police officer exactly) called us up and said my husband was eligible for the 居住证. My husband is a musician, self-employed, and under normal circumstances would be unlikely to qualify for a 居住证, but this guy was saying things like "you won't qualify without me." We had a strong suspicion he was fishing for bribes/hong bao and my husband got kind of pissed off at the implication and was sort of rude to the guy on the phone. Oh well, guess we won't be legitimate Beijingers anytime soon.