Another word you might consider is bolster. It's a verb meaning "to strengthen or support."
This verb is often paired up with the noun claim, as in these news articles:
A number of studies published in reputable journals and backed by the beverage industry have sought to bolster the claim that artificially sweetened beverages can prevent a person from packing on extra pounds. (Newsweek)
He also claimed that notebooks were doctored to bolster the claim that Brown wrote the script. (Variety)
To bolster the claim that the "loss" wasn't that bad, The Times points out that Google sold Motorola Home for $2.4 billion and is keeping most of Motorola's patents. (Mashable)