Unfortunately, neither Community Catalyst nor RIte Care Works, the author and promoter respectively, seem interested in providing the full details behind a press release from The Clarendon Group that appears to support the conclusion that every dollar of RI government money taken from RIte Care comes with a 12¢ cost in economic activity but save Rhode Island — overall, not just its government — 14¢:

The report from the national non-profit advocacy organization Community Catalyst, broke down where the dollars cut from the RIte Care program would go:

• 52-cents of each dollar stays with the federal government rather than making it to Rhode Island in the form of federal matching funds.
• 35-cents of each dollar is shifted to the private sector in the form of high-cost uncompensated care that’s ultimately left to hospitals, insurers, and premium payers to pay.
• 6-cents of each dollar is lost in reduced state tax revenue that is no longer being collected on the economic activity associated with the lost federal matching funds.
• ONLY 7-CENTS REMAINS AT THE DISPOSAL OF THE STATE AS “SAVINGS.”

Clearly, the authors are measuring “the state” more broadly than just its government, because they include the cost “shifted to the private sector,” and surely a failure to merit matching funds doesn’t shift to the expense column (for the government) in addition to being erased from the revenue column. What’s notable about the findings is that money is saved even with this broad analysis.
On the other hand, they don’t give the cost of lost economic activity, just the taxes on it, so the proper interpretation is probably that our analysts stirred a bunch of quick calculations in an activist pot until they arrived at a mixture that they thought to be salable.