Not true ... all LEGAL immigrants are screened medically.
People on immigrant visas are, but people on other types of visas are not. My husband's IR1 visa (unconditional green card) was issued a short time ago and he had to submit proof of vaccinations, give blood for an HIV test, and have a chest xray to rule out TB. The US government makes all visa applicants in the UK use the same private surgery in London, so it's not free either. All legal immigrants all over the world have to jump through these hoops and now that we've been through the process I'm even LESS tolerant of illegal immigrant whining than I was before.
We have medical screenings for a reason.