According to 99% of the history, archaeology and anthropology books I have had to read over the last decade(s) that is not true with humans. Typically according to most scientific research I have seen indicates inbreeding within the first generation often produces expression of recessive traits which is where the abnormalities come in. I have seen nothing that indicates up to and after 8 generations would do this to any significant way.
Current inbreeding laws in most countries also reflect this, most limiting to first cousins, though, in many states and countries this is allowed. I have never seen a single country/state define inbreeding as 8th or 9th cousins and if it is done it would be the exception not the rule, likely from this old custom. Since they mostly enforce these laws likely to prevent such bad gene combo's I highly doubt that this an issue so far removed.
The relation to tigers and nobility or royalty is rather/completely different. 1-5k is hugely different for royals marriage pool as I mentioned above. There likely were hundreds or, thousands of them if including cadet lines, in all Europe true but they were not limited to just marriage to this group but the nobility and at times even outside this even. Marriages are made between new noble families in the 14th and 15th further increasing the gene pool so to speak. As I said earlier, this topic has been often enough been researched that it is not something that needs guessing at only looking up one of many decent books on medieval marriage or marriage practices.
As I mentioned earlier it becomes more common later to marry first and second cousins but not so much in the medieval, though it happens at times. 1st cousins is where you'd likely see genetic issues... some in the secondary but every line out is another massive jump in the unlikelyhood of any abnormal traits appearing. A fairly recent study in Iceland showed no(few) abnormal issues with 3rd and 4th cousins and that they actually had many benefits (Not advocating this BTW but there it is). You can see it from the Journal Science of either Jan or Feb 2008 cannot remember.
If those would like to continue this topic would mind switching to the pm so we do not hijack this thread further I can find/provide all the info needed.
There ain't nothin' girlie about a tunic...