Your interpretation of (1) is incorrect. The records compared are not round-robin head-to-head, but total records involving all 3 teams.
In which case, currently the records are:
SA: 3-5 (2-1 vs HOU, 1-3 vs PHX)
PHX: 5-3 (3-1 vs SA, 2-2 vs HOU)
HOU: 4-4 (2-2 vs PHX, 2-2 vs SA)
Therefore the tie is indeed broken and the order is PHX-HOU-SA

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