There is $14,000 per receiver per year federal gift tax exclusion limit while sending money from the US to India. From a legal stand point, how can I establish that I am sending the gift amount to some person (e.g. my mother), and not to someone else? Technically, one can split $28K equally between his/her parents, and still that should be counted as tax-free gift transaction. If I ever need to testify the same, how can I do that?
You are (not the receiver) under the obligation to file for gift tax if you go over the limit, and the IRS would never know about the gift at all if you don't file.
If you in your mind declare the gifts are 14000 for the parents each (note, the limit is now 15000, actually), that is perfectly legal (and an expected and quite common use of the limit).
If you ever get audited, it is up to you to make a convincing case - if you declare you gave everyone in the village the parents lived 14000 (and they just happened to hand it all to your parents), it might not be very believable, but giving each parent separately 14000 is an obvious and believable claim. You could even send it in two pieces, with two names on them, and nobody will doubt you.
If you are using normal banking channels -- wire transfers, bank-provided services such as Remit2India or Money2India, or even things like Xoom -- you should be getting a transaction receipt showing who you sent money to on your screen soon after hitting "Send Money" on your keyboard. Print out this receipt and save it in your tax documents file, or save it as a pdf file in a folder marked "Important Tax Documents -- DO NOT DELETE" instead of just closing the screen while patting yourself on the back for your dutifulness as a son. Depending on your operating system, perhaps locking the file to prevent accidental deletion might work too.