[RPG] Who can use magic scrolls

Yes, the wording does mean that a cleric of the Light Domain gains 'Fireball' as part of the Cleric Spell List; and here's why the wording is different. I hope the following helps explain why

"The following spells are added to the warlock spell list for you," which shows that Fiend patron warlocks have Fireball in their spell lists, and so should be able to use Spell Scrolls of fireball.

The above Warlock phrasing, just as it's phrased for Wizards and other spell casting classes that gain extra spells through means of specialization, is phrased that way because each of those classes have a spell list that they must choose spells from as they level up. They do not inherently know all spells available to a Warlock. So the phrasing in this case means the fireball spell is added to the list of spells he can POTENTIALLY add to his 'Spells Known' list. For intents and purposes, those are now on his Warlock Spell List

Now enter Cleric, and the Paladin; which have very different methods of spell learning.

If you have a domain spell that doesn't appear on the cleric spell list, the spell is nonetheless a cleric spell for you."

It must phrase it like this because Clerics and Paladins do not have to choose what spells they learn as they level. Clerics and Paladins inherently have the knowledge of every spell on their list....because we're awesome like that....and can prepare spells as needed in between long rests. If I wanted to go with cure wounds one day and then give up cure wounds to take Inflict Wounds after a long rest? I can do that freely. I have direct access to every spell available to Clerics. So when I choose Light Domain and it says the Fireball spell that isn't on my class list nonetheless becomes a cleric spell? It's now part of my knowledge of cleric spells (On my list of spells), and thus able to be utilized in scroll form since I now have the knowledge of how 'Fireball' works magically.

The only reason it doesn't say these spells are added to your spell list for you, is because it wouldn't matter in a Cleric or Paladin's case. Any spell that's on our spell list is a spell we can cast should we choose to. Any spell that's on a Warlock/Wizard/Sorcerer spell list, is a spell they can cast only if they chose it from their spell list when gaining levels.

This has been addressed in the latest Sage Advice.

Thank you, @V2Blast

Sage Advice

Does the Thief’s Use Magic Device feature allow them to use spell scrolls?

Yes. The intent is that a Thief can use spell scrolls with Use Magic Device.

DMG page 141 is also of some help here (Casting Spells):

The ability check is still required to cast from the scroll but, as a Rogue has no spell-casting ability score, their's is always treated as zero when casting spells from magic items. It would stand to reason that a check would be in order to cast the spell from a scroll as well, the only issue is that it is just a d20 roll for them.

If you don't have a spellcasting ability—perhaps you're a rogue with the Use Magic Device feature—your spellcasting ability modifier is +0 for the item...

It does go on to say that your proficiency bonus (PB) does apply but this is specifically called out as an ability check so your PB does not apply to those. If it were a Wand or Staff, is what I believe the PB is intended to use.