Your 6th World may vary.
His squad were burned. The corp have burned him. Burning an asset, to me, means that they've tried to kill them/get them killed, disavowed all knowledge and destroyed all records (except for super-secret records). The corp isn't looking for him; or if they are, they only started after they burned him. Too late now to say "Whoops, yes, sorry Lone Star, that guy we said wasn't one of ours: turns out he was."
You're still looking at this from the wrong end. If you want to burn an asset (or ruin someone's life), rendering them SINless is a good move. You take so much from them by doing so. And if you're a corp suit with access to the corp SIN database, it's easier to delete the SIN that to hack LoneStar to add a criminal SIN.
I suppose you could alter the corporate SIN data to show an internally-deal-with criminal act, but you'd need more paperwork and I'm not sure the 'Star would treat a Corporate Criminal SIN the same way as a standard Criminal SIN.