I was a long term ranger at WW for ten years, working with Alvin and other regular rangers.
Actually, the WW regs don't require the major/minor first aid kits like on the Grand. In fact, as noted, the regulations don't specify the contents of a first aid kit (The stipulations require, "a first aid kit adequate for the size of the group and type(s) of activities, and sufficient for treating serious injuries). So I approached it from the point of view that -- beyond a few basics -- I really wasn't going to be very intrusive in my inquiry. As long as they gave me a reasonable belief they had a basic on-river response capability, I tried to be flexible.
In most cases, I'd ask to see the container for the first aid kit, and when they produced it, I'd ask if anyone on the trip had formal first aid/medical training. Depending on the yes/no there, I'd ask either that person or the TL if they were familiar with the contents of the kit. I'd then ask if they were comfortable with using those contents in any reasonably foreseeable situation, based on the length and complexity of the trip, the river conditions they were expecting, and the size of their group.
Only rarely did I get a questionable response, and only rarely did I go farther than that. Going farther might have involved asking to look in the kit itself, but in most cases it was just to ask the TL or trained person to tell me what they had in the box.
Because there were no real official BLM standards, I was never quite sure how I'd have handled it unless they had nothing at all. (In a few cases where the kit was forgotten at home, they went back to Grand Junction to buy something; at least once they borrowed a spare kit from another party launching with them.) But in that context, I approved kits for a day kayak trip that were very, very basic. And I also once approved a kit carried by a full-on doctor, who told me his kit included suture packs and IV supplies -- that was his comfort level for an overnite summer trip through WW.
I'd say if you have a readily identifiable kit, with sensible basic contents -- bandaids, antiseptic, compresses, ace bandage and other wrapping material, asprin/tylenol/ibuprofen, and maybe a few other such items to stabilize an injury until you get to Cisco, you're going to be good to go.
If you have any real questions, there's always the option of calling the Moab field office and getting a more authoritative response.