Ok, got it. That is helpful.
First, I agree with your board's decision to ban the one-off use of external, team-provided equipment.
Second, let's discard the bits from your question that are irrelevant to the issue:
They are a stacked team and nobody in our league will beat them no matter what ball is used
This is not germane to the issue at hand, so that fact should be removed from/not considered by the grievance committee when making and handing down the ruling.
Now to the crux of the issue; The one "oddball" pool table which uses a non-standard cue ball. Few thoughts and questions on that:
Can that single different pool table (or the venue which owns it) be swapped out for another? Many leagues make the rules on the equipment (and thus, don't have the need to write rules on bringing one's own cue ball). If a venue wants to host the pool league, they must have equipment that complies. I would strongly encourage looking into this. It just makes sense longer term, and makes everything consistent.
If the other team thought to bring a standard-sized cue ball, it must mean that it would work fine in that particular one-off pool table. This begs the question: Why doesn't the venue just swap out the cue ball for one that is of the proper size, permanently? Again, this would bring consistency to your venue roster.
Either of the above solutions would mean you don't have to take either team's side on the issue. I would expect the teams to fully understand the need for consistency.
Again, the reason you aren't really finding any written regulations on bringing one's own equipment to a match is because that type of thing is typically regulated via tournament equipment standards rules, and venues must comply.
Here is the WPA spec which deals with balls. BCA's would be similar, if not identical:
- BALLS AND BALL RACK
All balls must be composed of cast phenolic resin plastic and measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter and weigh 5 ½ to 6 oz [156 to 170 gms]. Balls should be unpolished, and should also not be waxed. Balls should be cleaned with a towel or cloth free of dirt and dust, and may also be washed with soap and water. Balls contaminated with any slippery substance – treated with a polishing or rubbing compound and/or waxed – must be cleansed and dewaxed with a clean cloth moistened with diluted alcohol before play.
If the pool table and accompanying balls don't comply, that table/balls or the venue should be taken out of the league rotation.
Hope this helps in some way.
Let us know how it all turns out.