It's not just an "opinion".
Go back and check the Rulebook.
Support comes in "2. Calculate Initial Combat Strength"
When you get to "5. Calculate Final Combat Strength" it says:
Both sides now combine their initial Combat Strength with any modifiers accumulated by playing House cards and using theValyrian Steel Blade token. This final value is referred to as a player’s Final Combat Strength.
Below is a summary of what could contribute to each player’s
final Combat Strength:
-- Initial Combat Strength *
-- The Combat Strength and applicable text abilities of the chosen House card
-- The Valyrian Steel Blade’s +1 Combat Strength (if available and used)
* Some House card text abilities may cause a player’s initial Combat Strength to be recalculated. For example, if the text of a revealed House card destroys an opponent’s Footman unit, the initial Combat Strength of that opponent is reduced by 1 during this step.
Since Initial Combat Strength has ALREADY been calculated (and Support included), it CANNOT change unless a House Card does so.