> A good government wants the population overall to be in good health, and has a budget within which it must operate. It may make more sense for the government to ignore your rare disease if detection/treatment is expensive, and that money can be better used to save, say, 10 people with a more common disease.
That happens on the research funding side (e.g. it makes more sense to spend research money on cancer or heart disease than on an obscure disorder that only 10 people have).
However, it's not true that the government will provide misinformation or otherwise get in the way of diagnosing your rare disease to save money.
There are a lot of studies about the cost/benefit tradeoff of early diagnosis and preventative screenings. The goal isn't to reduce healthcare expenditure, it's to reduce problems and deaths from unnecessary procedures and treatments. We learned a lot from previous eras of over-treatment and over-testing that led to a lot of unnecessary treatments due to false positives. The risks of over-treating can actually outweigh any benefit of excessive testing, for example.
This is counterintuitive to individuals who want to order huge numbers of tests all the time just in case something might be wrong. The problem is that a lot of diseases may have occurrence rates on the order of 1 in 10,000 or 100,000 per person-year, while the tests may only be 98% to 99% accurate. This 1 to 2 in 100 will be misdiagnosed as false positives and potentially put on expensive medications or treatments that have negative health consequences. It's a very real problem that isn't obvious from the individual level but becomes very obvious at the population level when you start looking at the details.
But no, the government isn't actually hiding information about diseases or misleading people in an attempt to reduce costs. With many conditions it's actually much more expensive to be diagnosed later in the disease than it is to be diagnosed earlier when many conditions are more receptive to treatment.