Would Medicaid from the New York State of Health make me a public charge?

[Da&Lu]

I am a third-year permanent resident, in New York. Could I apply for Medicaid through the New York State of Health without becoming a “public charge”?

I discovered that state health care might not make me a public charge; that would apparently get me a normal insurance card, rather than a federal Medicaid one. These pages indicate that I can receive Medicaid as long as I am not institutionalized for long-term care:

[1] http://www.uscis.gov/green-card/green-card-processes-and-procedures/public-charge
[2] http://www.communityhealthadvocates.org/publications/advocates-guide/section-11a-%E2%80%93-immigrant-eligibility-new-york-state-health-insurance#1b

Is my assessment accurate? Could I apply for Medicaid through the New York State of Health without making my sponsor liable for my medical bills? Thank you!