Your brother is very wrong, as the others say - the EHIC covers basic immediate medical care, not hospitalisation or repatriation if your SIL needs to fly home. Hospital care overseas can rack up costs, as can medication. He must declare her condition when taking out insurance, otherwise anything to do with that condition won't be covered.
Bearing in mind that travel insurance also covers loss of baggage, theft of cash, etc., they would be taking a huge risk to travel without it - if she's ill away, the costs of caring for her and/or getting her home could run into five figures at least.
Eddie, no airline has ever checked my travel insurance - do you mean, under tinker's SIL's medical condition they wouldn't let her on the plane? - if it's not declared, how would they know?