It's not a coincidence that Rockstar made Downs stopped Arthur from the bar fight. Of course Arthur had been contaminated by Downs from a bar fight.

However, Arthur always felt guilty for collecting money from poor people. He didn't like it. So he want to believe that he got disease from Downs when he punched Thomas Downs to death to collect his money. That's why he kept helping Mrs Downs and his son. He wants his redemption so much. That's why he told it to Sister Calderon. He didn't recognized that he was already got it from bar fight.

Next, if he didn't go to Guarma, his sickness may have not been came so early, or he disease may never came out. Because in Guarma, he got so weakened he started dreaming his symbolic animal: a coyote or a stag, and eventually the sickness came out after Guarma.

If only Arthur run away with Mary to New Austin or Mexico without going to Guarma, he wouldn't have died with tuberculosis early. Because New Austin/Mexico is dry and warm. He would have been fine so long.