Not true, because those were individual kingdoms which operated under a different set of rules. Each of the seven kingdoms still technically has their own royal bloodline. The Martells still rule Dorne and though they are not given title of king of that kingdom, there bloodline is the royal bloodline of that land. The Targaryens were the first to bring the kingdoms under one rule and are the true kings of the seven kingdoms, a position that did not exist without them. There blooldine is the royal bloodline for that title. The two fall under different rule sets.
That's not true at all. There is no 'separate kingdom', and there is no royal bloodline for each region. They lost the royal bloodline when Aegon conquered them, be it through annihilation, like the Riverlands and the Reach, battlefield defeat, as it was for the Westerlands, peaceful submission, as it was for the North, or diplomatic parley and reconciliation, as it was for Dorne. If it was, then who the hell is the royal family of the Reach? The Tyrells? They were the stewards of the previous Kings of the Reach, House Gardener.
House Gardener was wiped out in Aegon's Conquest. The Tyrells were named the lords of the Reach in return for their fealty to the Targaryens. Same with Harren Hoare and House Hoare. They were the Kings of the Isles and the Rivers (aka the Iron Islands and the Riverlands). They were wiped out when Aegon rode his dragon on Harrenhal (you know, the big burned out castle) and destroyed the entire house. That's were the Greyjoys were elected as the lords of the Iron Islands, and where House Tully was named the Lords of the Riverlands.
The reason any of the houses still rule their respective regions is because they submitted to the Targaryens and were named the Lord Protectors of their region of the realm. They aren't 'royalty' anymore, they're nobility. Dorne is the only house that omits the Lord/Lady titles for the Prince/Princess titles because they were the only region of Westeros to not technically be conquered by the Targaryens (and were able to negotiate their own submission to the Crown on their own terms, one of which was the right to retain the Princely title that they had always used.)