It sounds like you already understand this, but since you talked about targeting bricks in the first post, I just wanted to clarify.
When something looks for lowest/highest facility, the amount of the resources you have doesn't influence the decision. Likewise, when something targets a lowest/highest resource, it doesn't take the value of the facility into consideration.
There's no tiebreaker. It really is an even chance among the valid targets.
This can also be confusing when a keyword effect changes the value of a facility since that change occurs AFTER the card effect is concluded.