After Estelle puts the Lexi name tag on Shane, the angle changes in successive shots.
Shane tells Thomas that up until 6 weeks ago she was Shane Walsh. The news reports said she had died, but in fact she was missing, and after only 6 weeks would not be pronounced dead but would still be listed as missing.
Matt was clearly well to do and could have used a private investigator to locate Shane, which would have taken less than a day with the information he had discovered. There was no need to gank the zip line dude.