Yes; the ruling is now official and explicit from Sage Advice

As Dale M's previously-accepted answer said, the PHB rules for the Arcane Trickster imply that its class spell list is the Wizard's spell list.

This was made explicit in the official Sage Advice, which says:

For you to meet a spell scroll’s requirement, the spell on the scroll needs to be on whatever spell list is used by your class. Here are two examples. If you’re a cleric, the spell must be on the cleric spell list, and if you’re a fighter with the Eldritch Knight archetype, the spell must be on the wizard spell list, because that is the spell list used by your class.

From the example of a Eldritch Knight, we know that there is no class list of spells for the fighter class, but the class list for a fighter that becomes an Eldritch Knight is the wizard class list. We can conclude that there is no class spell list for rogues, but a rogue that becomes an Arcane Trickster has the wizard spell list, "because that is the spell list used by your class."

Thus an Arcane Trickster can use spell scrolls of spells that are on the Wizard spell list.

Thanks to InternetHobo who encouraged Rubiksmoose to cite the SA Compendium in their answer.

It does not, you must roll the Ability Check

Multiclass spell slots for a wizard/cleric are determined by the multiclass rules on Page 164 of the PHB (emphasis mine).

If you have more than one spellcasting class, this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower-level spells. If a lower-level spell that you cast, like burning hands, has an enhanced effect when cast using a higher-level slot, you can use the enhanced effect, even though you don’t have any spells of that higher level.

This allows you to HAVE higher level spells slots than spells you actually know. But, it also stipulates that you cannot cast a spell of that level from one of your classes but can only upcast lower level spells you actually have.

But why?

Because there is a difference between spell slots and what you can cast due to the Multiclass rules.

As you also stated, the spell scroll rules only state, emphasis mine (DMG, 200)

If the spell is on your class’s spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully.

You have a 5th level spell slot, but you cannot actually cast any 5th level spells. He can neither prepare nor know any 5th level spells. What he can do is upcast a spell he can prepare/know in a 5th level slot. What they can prepare/know is going to be specified by their level in that class.

Crawford confirms

Jeremy Crawford answers a question multiclassed spellcasters and casting from scrolls.

Here is the Q&A:

Q:Cleric 1/ wizard 9, find Scroll of Greater Restoration, need WIS check to cast or having 5th level slots count for it?

A:As a multiclass spellcaster, the spells you can cast are determined for your classes separately. In the example below, make the check..

The case of the scroll and a Cleric 5/Wizard 4

In the case of a scroll, it would work as stated above. You have a 5th level spell slot, but neither of your cases actually enable you to cast a 5th level spell. In order to cast that 5th level spell, you'd need to roll the ability check.

It is clear that you have 5th level spell slots, and I believe it is a reasonable interpreation that you can not cast 5th level spells due to the specific limitation in Multiclassing of "this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower-level spells"(emphasized in block quote at beginning of answer). A 5th level spell scroll would be off-limits as an automatic cast because of this.

A Cleric 5 can cast 3rd levels spells and a Wizard 4 can cast 2nd level spells.

Combined, you have 4th and 5th level spell slots, but you can only cast up to 3rd level cleric spells or 2nd level Wizard spells. In order to use those higher level slots, you could only upcast the spells you can actually cast.

Spell Scrolls with a cleric spell of up to 3rd level would be auto-cast. Spell scrolls with a Wizard spell of up to 2nd level would be auto-cast. Anything higher than either of those would require an ability check.

You have a 5th level spell slot but cant actually cast 5th level spells as a Wizard or a Cleric. You simply can't cast 5th level spells and having a 5th level spell slot doesn't change that.

Your specific casting class must be able to cast the spell.

Upcasting?

One potential problem comes with the information presented on Page 201 of the PHB:

When a spellcaster casts a spell using a slot that is of a higher level than the spell, the spell assumes the higher level for that casting.

This seems to imply that 'assumes the higher level for that casting' means that what was once a 2nd level is now a 5th level spell due to the upcast. The problem with this General rule is that it breaks in the face of the Specific Rules of multiclassing, which say you can't cast spells of that level, but you can upcast with that available spell slot. This shows that you don't actually have access to 5th level spells, but can use that slot to upcast and upcast only.

The rule on page 201 is less about you being able to cast higher level spells and more about how to treat an upcast spell when facing a counterspell/dispel magic or something else where the spell level is important. Because of the specific requirements around Multiclassing, it is clear that you can not cast 5th level spells as a Cleric 5/Wizard 4.

Specific beats general?

Usually, we can go with an analysis of Specific beating general. However, in this case we have two specific and competing rules (multiclass spellcasting rules and Scroll Casting Rules.)

The only suggestion as to which is more specific lies in the fact that the spell scroll rules are not assuming a table has engaged the Optional Multiclass rules and was likely written assuming single class which would remove any doubts as to whether or not to roll the Ability Check. Once Multiclass Rules were engaged, they became the specific to override the general casting/Scroll Casting rules.