Can anything be done when denied boarding due to missing but not required visa?

"Transit" means many things, depending on who is describing it:

1. You are flying on one airline, on one ticket, and are just changing planes.
2. You are flying on one ticket, but different airlines (called codeshare) and are changing planes.
3. You are traveling on two different tickets, on the same airline, and need to get a boarding pass.
4. You are entering a jurisdiction that requires transit visas no matter what the final destination is (for example, UK, Schengen Zone, US, etc.)
5. You are traveling from A to B on one airline, then from B to C on a different airline.

You may call all the above transit, but for the purposes of visas, not all transits are the same (and some don't qualify as transit at all).

In all these situations, transit requirements are different and to make matters even more complicated, your nationality may also have an impact on visa requirements.

One way to confirm what is required is to check the Timatic database, which is what airlines use when determining eligibility to fly.

According to Timatic:

Transit - Ethiopia (ET)

Visa Visa required.

TWOV (Transit Without Visa): Holders of onward tickets for a max. transit time of 12 hours.

Visa Issuance: Passengers can obtain a transit visa at Addis Ababa (ADD) if transit exceeds 12 hours and if they have confirmation that a visa has been approved before departure by Ethiopian Airlines. The maximum transit time is of 24 hours.

Now, your specific situation:

They booked two tickets to travel on two separate airlines and have a 4 hour transit in Addis Ababa.

This means that you need to be landed in Ethiopia, because you are actually on a two-part, point-to-point journey.

One leg of your journey requires you to arrive in Ethiopia, go through immigration, collect your bags, go through customs.

The next leg is for you to walk upto the check-in desk in Ethiopia, collect your boarding pass, check your bags, go through immigration.

So you clearly do not qualify for a TWOV (Transit Without Visa); as you are not in transit (you don't hold an onward ticket).

If you do not have a visa (or otherwise do not require one) the airline is right to refuse you boarding; as you do not qualify for the transit-on-arrival visa since it is only issued for transits more than 12 hours and from Timatic, seems only if you are flying on Ethopian for the entire journey.