EEA2 application denied. Appeal or re-apply?

[luchoilo]

Hello, I'm a student, with EEA nationality. My wife (non-EEA) has been here in the UK since April on a EEA-family permit, and we applied to the EEA2 RC, which just got refused. The reasons are that they considered I failed to supply evidence of a comprehensive health insurance, and that I failed to provide evidence that i have sufficient resources "not to become a burden" to the UK. I'm quite confused since I provided the EHIC as health insurance, which according to the guidelines of the application is valid if I aim to stay in the UK temporarily. Since I'm studying a Phd, and have no intentions of remaining here after I finish, I think I am temporarily here, which I explined in a signed declaration. Also, I provided bank statements of 4 months, that demonstrated that I am recieving my bursuary/studentship, around 1500 pound a month on average. I am really confused: should I appeal, or re-apply? Am I missing something, or the HO descition is against regulations?

Thanks a lot for your help.