ORISE fellowship program and Health Insurance Costs

Imaginary numbers/real scenario:

My stipend (base/net pay) is $5000. For 2016, I selected the ORISE health insurance plan (cost = $1000/month) because it seemed like the best deal (initially)- great coverage and ORISE paid for it. The amount of my stipend, and thus my “gross pay,” is now $1000 more a month ($6000), which I'm afraid is what I will be taxed on. This increase in the stipend amount results in an increased year end gross pay total, and a considerably higher amount (~$200/month) tax bill.

Because ORISE is not my employer, I can’t claim that the added $1000 is not a wage and thus not taxable, as this blurb from IRS page on Employee benefits says:

“if an employer pays the cost of an accident or health insurance plan for his/her employees, including an employee's spouse and dependents, the employer's payments are not wages and are not subject to Social Security, Medicare, and FUTA taxes, or federal income tax withholding.”

But how can my health insurance costs, regardless of whether ORISE pays them, be taxed?

I looked at the IRS Pub 970 as well, but saw nothing regarding health insurance premiums. Am I now responsible for paying taxes on the added amount to my stipend, even though it goes to health insurance costs? Or is there a way to deduct it?