"As opposed to employer "sponsored" plans ."

There is no "opposed to" in the SEHI. The word "subsidized" is applicable to more than one thing. ACA/State marketplace plans (which by definition are not employer group plans) are using the word differently than the SEHI requirement that it not be an employer-subsidized plan.

Here is an example that I think helps: Employer A does not offer health care coverage. They do have a reimbursement policy for the employees who get an ACA/marketplace policy. Other employees might have coverage through their spouse's employer B as a family plan. So, if your taxpayer is married to an employee of A, there i no employer plan on offer ("subsidized" is moot, there is not even a plan). If your taxpayer is married to an employee of B, there is a family plan available (group plans are typically subsidized). And I was remembering historically, a lot of this came about in regards to COBRA coverage, which was an unsubsidized policy price, typically, but was through the employer.

Check this link:

https://turbotax.intuit.com/tax-tips/health-care/what-is-employer-sponsored-coverage/L01gcZpTR