The .223 Rem can be extremely accurate/precise if set up properly with heavy (80-90 gr) bullets.  Whether it possesses intrinsic BR-level  accuracy is another story.  Here are a few target images from one of my .223 F-TR rifles set up to shoot 90 VLDs (30" 7-twist 5R Bartlein barrel, 0.169" freebore), all shot from a bipod/rear beanbag:
		
		
	
	
5-shots @ 100 yd
5-shot groups @ 100 yd (Seating Depth Test)
15-shot group @ 300 yd
15-shot group @ 300 yd (< 0.5 MOA)
2x20-shots @ 620 yd (3" and 6" scoring rings)
IMO - the keys to shooting heavies in the .223 Rem are:
1)  having sufficient barrel length (28" to 30")
2)  having sufficient freebore (minimum ~0.120" for 80s, minimum ~0.169" for 90s)
3)  rigorous seating depth testing in small (</= 0.003") increments
There are several ~90 gr bullets from which to choose; Berger 90 gr VLD, Sierra 90 gr Matchking, Hornady 88 gr ELDM.  H4895 and Varget are good powder choices.  90s over H4895 will usually tune in around 2850 fps from a 30" barrel.  Brass life is generally very 
poor (</= 3-4 firings).  All the targets above were fired with 90 VLDs over H4895 at about 2850 fps.  Varget will usually tune in about 20-30 fps slower than H4895 and may provide slightly better brass life.
Loads with ~80 gr bullets such as the Berger 80.5 Fullbore and 80 gr VLD, Sierra 80 gr Matchking, Hornady 80 ELDM can also be loaded with equally outstanding accuracy/precision.  In fact, loads with the 80s may be much better in terms of brass life.  However, they do give up a certain amount of resistance to wind deflection at longer ranges.