Why high quality DNA should be between 10 and 20 kb?
The website specifically talks about DNA samples intended for sequencing. The DNA in these samples was/is/will be extracted from cells and this extraction procedure leads to fragmentation (breaking into chunks). Since the expected average chunk length will greatly depend on the extraction process, I guess its reasonable to assume that 10-20kb can be expected from the most common protocols. 

Much larger or much smaller fragments will also cause problems with the sequencing. (This is again method dependent, but generally true with varying fragments sizes that can be sequenced with the different available methods)