Hi Puru
Thanks for your question. I am not involved in NASA in any way, but after going through a few links - as well as NASA's own site - I haven't found any evidence for this. It seems like there was a flurry of posting and re-posting about half a year ago on this topic but there are no primary sources to be consulted, just a large echo chamber. Within this echo chamber, people are certainly referencing the Briggs article, but not so much the fact that it was written almost 30 years ago.
I also don't know where this "he invited 1000 scholars to participate and they all refused" garbage came from. Not only is there no reason for Sanskrit scholars to keep their knowledge "rahasya" but I am sure that Sanskritists would be thrilled to have the language more widely disseminated. As it is, the only Skt daily newspaper is currently desperately seeking funds to remain in print (although it will conitnue publishing on the web, that is not in question).
Furthermore, there is no page on NASA's site that references Sanskrit, let alone "Mission Sanskrit," aside from mentions of the Chandra observatory and the Kālidāsa Crater, the connections there being obvious.
Briggs's article was a fascinating thought-piece but I don't think it has gone any further than when it was published in 1985. However, I am open to having my mind changed, hence I am posting an answer that is only to the best of my knowledge, in the hopes of inviting other contributions to the discussion.