You can "accept" anything you want! Well, within reason.
However, term policies offer no tax advantage to the donor. And there isn't a legal gift with these - no cash surrender value and premium payments are not deductible. The only value they have to a nonprofit organization is if the donor dies during the "term" and you realize the proceeds.
As to what your colleague heard, that applies only to whole-life policies that you own and are the beneficiary. In that case, the donor can make payments directly to the insurance company for your premium payments. The company acts as your agent. However, you must obtain proof from the company regarding who made the actual payment. You will need a copy of the canceled check or credit card statement. Your receipt must reflect that entity's name.
Frankly, it is much cleaner if the individual makes a gift to you rather than pay the company.
John
John H. Taylor
Principal
John H. Taylor Consulting, LLC
2604 Sevier St.
Durham, NC 27705
919.816.5903 (cell/text)
Serving the Advancement Community Since 1987