I was unaware of this rule about a year ago and attempted to enter the LGA UC with a guest who was flying on DL. The guest scanned his BP at least twice and it was rejected. The agent seemed perplexed until she looked at the BP and realized it was DL. She then advised that guest had to be flying UA but let the guest in as "an exception" because the lounge was pretty dead. Would not count on that happening very often.