The EHIC card is for sickness insurance if you travel abroad to another EEA country. It is not for use in the country from which you obtained it.
For example, if I obtain an EHIC card in the UK as I am a UK resident, it would only be for use in another EEA country such as Spain, if I required health treatment there.
If you are resident in the UK and seeking health care in the UK, then you would normally use the NHS. The NHS has its own rules about who is entitled to NHS care, see here for example:
http://www.dh.gov.uk/en/Healthcare/Enti ... /DH_074374
So NHS rules could say you are legally entitled to be an NHS patient, but UKBA could say you shouldn't be an NHS patient.
The problem being the UKBA regard EEA self-sufficient / student applicants ( and their family members) who rely on the NHS for their CSI as being an unreasonable burden, as UKBA regard that as not being self-sufficient.
That applies even if the family members are working and paying National Insurance contributions and taxes to help fund the NHS.
This can lead to the unfair situation that EEA nationals who have EHIC cards issued abroad can use the NHS and be regarded as not being a burden even if they do not pay tax or NI, but family members of self-sufficient EEA nationals - who are helping to fund the NHS by working and paying taxes etc - being regarded as burdens, even if they don't use the NHS that they are paying for, and are legally entitled to use. It is crazy and unfair.
As explained, if someone is temporarily unemployed ( usually less than six months) they are still regarded as a jobseeker and a worker, so they usually do not need to supply proof of CSI.
The requirement for proof of CSI is for those applying as Self-sufficient or students ( and their family members).