Eligibility for Social Security Survivor Benefits?

My husband passed away at 37 years old last month. We have been together nearly 16 years. We have a young son and daughter together.

Today, during my phone interview for survivor benefits, I was informed that another person has also filed for benefits for her child claiming that my husband was the biological father of her 4 yr old. Oddly enough, she filed immediately after his death (which was accidental therefore was made very public by news media).

This other person has no evidence to support her claim, nor does her child's birth certificate list any name of a father. Secondly, the SSA office clerk even voiced that it was unusual for a single mother not to ever file for child support, if in fact my late husband was the father, rather she waited until he has passed and can no longer speak for himself to make allegations.

SSA did advise me that she has the burden to provide proof to support her claim, however, until she drops her claim then my children will receive 1/3 less benefits than they were originally eligible for.

My question is, can this stranger actually steal benefits due to our children, simply because she claims paternity of her child? This doesn't seem legal or ethical. We are a grieving family. The loss of my husband and my children's father is bad enough, then to be put through this. Any other similar situations? Can they actually get away with this?