I've always wanted to bench 100 over body weight but would always stall out or gain weight. For the last couple months I've been neglecting bench press only doing 3 sets of 12 a week of dumbbell bench press. I've been focused on training my back and shoulders instead. I tested last night and hit 255 without too much trouble and this was after 8 sets of OHP. That puts me only 10 lbs away. I wasn't expecting that. I figured my bench was going to be a lot lower from not doing any heavy bench in months. I'm guessing the back muscles must help a lot in bench. I've always thought of it as a chest/tricep exercise      

I've always been told that being able to use lats in your bench is very helpful for hitting big numbers.  More muscle groups working.  I dunno anything about the anatomy of it, but my bench press has always been by far my most superior lift.

This is a subject that can be looked at a few different ways.
One is that lat strength is a general quality to the bench. If you improve a general quality and see improvements in a specific quality (your bench) then one of two scenarios existed. You either are so weak at bench that literally anything will improve it. Which a 255 bench at 165 bodyweight while fatigued doesn't fit that bill. Or you had a general deficiency so great that it prevented further progress in the specific pursuit. A more easily understood idea, if the shoulder girdle is out of balance due to over benching, strength gains in benching will cease until the shoulder girdle is brought back into balance, which might untap previously suppressed strength.

The other way is that the lats/upper back are a very important benching muscle. Scott Mendelson benched 715 raw and said lats were 75% of the prime movers in the bench. I benched 300 raw and have an exercise science degree and say he is wrong (haha, I crack myself up with that one). In all seriousness though, I think there is a big gap between what is said and what is meant. I can not agree with the idea that the lats are responsible for driving the bar off the chest for the first few inches. That would require a concentric contraction of the lats, which if it was possible I think any barbell rowing motion with the chest parallel to the floor would end a few inches away from the chest. That being said I think the lats/upper back can help stabilize the involved bones of the bench press, which creates a more stable platform to press from. Probably not as important with light weights, probably very important with very heavy weights.

Chris Duffin has a video on lat involvement in the bench which should be the first result if you search "Chris Duffin lat involvement bench" which I don't completely buy into  but is very intelligent and makes me question my own beliefs.

I agree with this. I don't think a strong back helps you with the lift, except for helping to stabilize you. I will say that a good bench goes hand in hand with strong shoulders. Work your shoulders well, and you should see an improvement. Also, if you're going for strength, drop the reps. When I was putting up 405, I would do warmups all the way up, like 225, 275, 315, and 365, doing about 3 of each. It helped me anyway. But on normal work out days, I would do say 365, 3-4 sets of 4-6. , then try 315 for 3 sets of 8.

Make sure you have a spot. I always noticed that it was harder to get stronger without one. Maybe it was a mental thing, but I'm a firm believer that to go up, you need a spot, and that has nothing to do with safety, in this explanation anyway.

I agree it's the better stabilization that helps. I also felt like my shoulders were more stable. For years I'd do something like 12 sets of bench and then throw in 3 sets of rows so I probably was out of balance bad. My chiro told me I had really weak serratus anterior muscles causing my shoulders blades to wing doing pushups. Probably a result of too much bench. That's 90% better now.