There are plans out there that have "high deductibles," but this, in and of itself does not qualify it as a high deductible health plan (HDHP).  While it is possible for an HSA qualified plan to restrict some benefits, it MUST provide significant benefits to qualify both a real high deductible health plan and for health savings account.

For example, if you are looking at a plan that offers you significant in-patient care (something happens and you get admitted to the hospital) that covers your hospital room, meds, tests, more tests, more tests, horrible food, more tests, a visit from the doctor, bandages, surgery (you get the picture), but does not offer much in the way of care when you are not in the hospital (trips to the doctor for a sore throat, physical exams, and other out-patient care), it is a "faux" HDHP and is about as real as that Llama skin purse you are so proud of.