Was Shimei right to call David "a man of blood"?

Shimei says it twice: "you man of blood" (16:7) and "because you are a man of blood" (16:8) (tap blood). The charge he names is "all the blood of Saul’s house, in whose place you have reigned" (16:8). He doesn't say which blood he means, and the chapter doesn't say whether he was right. David doesn't answer the charge; he answers Abishai (16:10-11). What the books of Samuel have told so far: David would not kill Saul, "since he is the LORD’s anointed" (1 Samuel 24:6), and spared him a second time (1 Samuel 26:9); when Abner was killed he said, "I and my kingdom are guiltless before the LORD forever of the blood of Abner the son of Ner" (3:28); and he put to death the men who killed Ishbosheth, Saul's son (4:11-12). The LORD's word through Nathan charged David with Uriah's death, "You have struck Uriah the Hittite with the sword" (12:9), and Uriah was not of Saul's house. In chapter 21, which tells of a famine "in the days of David" without saying when, the LORD says, "It is for Saul, and for his bloody house, because he put the Gibeonites to death" (21:1), and David hands seven of Saul's sons and grandsons over to the Gibeonites, who hang them (21:6-9).