I am not sure why you were told this. Here is what could happen in Ohio. If there is a beneficiary named on the life insurance policy, the proceeds don't have to go through probate. The insurance company will distribute the proceeds directly to the beneficiary. If the estate is large enough to require a federal estate tax return (over 3.5 million for deaths in 2009, including the life insurance), then it is possible that the beneficiary may have to contribute to the estate taxes. If the estate is large enough to require an Ohio estate tax return (over $338,333 in 2009, not including the life insurance), then the life insurance proceeds are not part of the taxable estate and should not ever be subject to Ohio estate taxes.
If there is no beneficary on the life insurance policy, then the policy has to be probated and the proceeds become subject to the Ohio estate tax. In that case, there may be some estate taxes due from the proceeds.
In either case, the tax payment provisions of the Will have a bearing on who has to contribute to estate taxes. The proceeds are not income taxable to the beneficiary, so would never be reportable on your 1040.