Those anullments are legitimate and brings great peace of mind and soul.
It's not a question of legitimate annulments.
It's a question of whether a sacramental marriage ever existed.
No annulment can void a valid sacramental marriage, no matter how much you want to dance around it.
Granting Holy Communion to unrepentant adulterers, even without the paper "annulment", may give the sinners great peace of mind and soul. But it's a false peace and it's a mortal sin.