I am sure that when it comes to target shooting, and shooting the smallest possible groups, the best custom actions, barrels (especially barrels), etc. can and do make a difference. After all, that is a game where very small improvements in group size, or scoring, make all the difference. Just the same I have seen some reworked Remington actions that shot incredibly well, although these usually had very nice custom barrels chambered for cartridges that were well known for their superior results downrange. I own none of these, but I have seen them at work.
When it comes to hunting, other things matter much more to me. Here I want no custom action, and in general I do not want a rifle that has tolerances that are too tight. Those might be great on the target range, but not for where I hunt, and not for how I hunt.
Here I value rugged reliability over almost everything else. A rifle that works every time, no matter the conditions, no matter how bad the weather, no matter how many times I have fallen down with it or on it. I want a rifle that holds its zero and does not object to snow, ice, and mud and blood. I want a safety that I can trust to do nothing other than what I expect, no matter what. I want a strong extraction and ejection system. I want a rifle that feeds reliably, slick all the time, no matter how fast or slow I run that bolt, and the bolt handle had better stay on too!
I want a trigger that doesn't do stupid things like refusing to fire, or firing when a safety is let off. It does not need to be a lightweight trigger, a 3 lb trigger would be lovely. Just a good reliable trigger, not too light, one that can stand up to some bad weather. I need to feel it when my fingers are so cold that they will hardly bend.
I want a stock that fits me really well. And a low powered scope that is exactly where I expect it to be when I throw the rifle up in a hurry. And that scope needs to be ruggedly reliable too, although I understand that scopes fail more often than most people would think.
On top of all that, I want bullets that work really well, at bad breath range on out to more traditional ranges. They must not fail, because there may be a lot at stake. A whole lot. They don't have to shoot small groups, they just have to work.
With all of that said, it should be obvious that the issues I consider important in a hunting rifle do not revolve around Remington versus custom action. Nor is a lovely tight little wad of holes in the target the ultimate deciding factor.
Experience has taught me what I value in a hunting rifle. Part of that is also dictated by where I hunt, and how I go about it.
Other people have very different circumstances, and may reach very different conclusions about what they think they might want. Good for them!
At this point in my life, I know what I want. But other people are still learning, still experimenting, still discovering what this whole shooting and hunting thing is all about. Try what you want, build what you want, and figure out what you like and what works for you.
It can take a lot of years to get it all sorted out, but that is where the fun is at!!