If we paid a friend or relative for childcare, can we claim it as a gift for tax purposes?

If we paid a friend or relative for childcare, can we legally choose to consider it a gift? This older thread seems to indicate that this would be okay if both parties agree to consider childcare and payment to be independent events. I understand that we then wouldn't be able to claim dependent care credit on our taxes. 

 

Bonus question 1: Does it complicate things if there are electronic records describing payments as being "for childcare"?

 

Bonus question 2: Ignoring bonus question 1, could we do both in a year? Could some transactions be considered payments (just enough to use FSA funds) and other transactions be considered gifts?

 

Thanks.