Could you as the executor of your neighbors will also be the only person to benefit?

Yes. However, the will should be drafted by an attorney who specializes in probate to make certain the will isn't vulnerable to challenges. A testator has the right to choose their beneficiary. Generally, a will can only be challenged on technical grounds not because someone doesn't think it's "fair". The attorney may advise the testator to name a different person as the executor although it may not be necessary.