[RPG] Do Life Domain Clerics Gain Access to Any Non-Cleric Spells in 5e

The bonus proficiency is a domain feature. Domains are a class feature. The multiclassing rules state that you gain the class features when you get a new level in the new class. It then lists exceptions to this with channel divinity, extra attack, spell casting and unarmored defense. Domains are not listed, so it seems that the bonus proficiency is the more specific rule and you gain the domain proficienices.

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.