The barrel itself, and the quality of the chambering, are the two most important factors in building an accurate rifle IMHO.
Mass production barrels are exactly that...
I honestly have no idea what, if any, QC Savage extends to their barrels- based on what I've personally seen I would have to say none.

As mentioned, just about every one I've talked myself into borescoping has absolutely horrible chatter from the rifling button. If I ever got a blank like that from Bartlein, Krieger, Shilen, etc. I'd put it back in the tube and send it back where it came from. Nevertheless, most all shoot "well"- meaning sub-minute, and some much better. Goes to show it's not as detrimental as many presume.

To my point, without stringent QC you can't be sure that EVERY barrel will live up to the high standards that top-end manufacturers stake their reputation on.
Every blank borescoped. Every blank air-gauged and the bore lapped. This is why the top dogs have the reputations they do, and can get the $$ they charge. No smith (none with a brain, anyhow) will want to risk spending a day painstakingly chambering a barrel as precisely as can be done- only to have it fail to shoot due to a lousy bore.

When it comes to barrels, you can guarantee a tack driver if you spend the coin on the barrel and a smith that knows what to do with it (or a prefit from a quality manuf)
Or, you can roll the dice less expensively with a Savage- usually you'll be a happy camper if your expectations are realistic. If not, re-barrel it- because they can be done without a smith, you're hundreds $$ ahead of the game.

The most expensive Savage I ever purchased (I usually just buy the actions) was a recent .338 LM.
Barrel looks like sh**, but shoots 3/4 minute. In my mind, for a bit over a grand- I got a marginal (but safe) action, and a nice chassis that was worth the purchase price. If it didn't shoot, I was going to rebarrel it and it would have still been a good investment.

Keep in mind, if you're an accuracy "freak" like many of us (only accurate rifles are interesting, right?)- scour the pawnshops and pick up a rifle in your desired action length- usually $200-$300 tops will do it.
You can rebarrel it, install a quality trigger, and set it in a decent stock like a B&C and still be at around a grand. In my mind, that's a better route than rolling the dice on a factory stick.