From your link on the TreeView (MSDN)
Gets or sets a value indicating whether the selected tree node remains highlighted even when the tree view has lost the focus.
If you have multiple TreeViews on a single page, you might want to highlight only the TreeView having focus. Otherwise the user wouldn't know which element is currently selected. But that's the only reason I can think of. Probably this is a designer error of this particular control?
You can test AccessKey in Teleriks Demo page where you get this result:

The demo displays the HideSelection property set to false, which I think should be default instead of true, as documentation says. This issue have also been answered on Stackoverflow C# WinForms highlight treenode when treeview doesn’t have focus.
TVS_SHOWSELALWAYS/LVS_SHOWSELALWAYSare explicit style flags you have to set. They inherit their default state probably from theES_NOHIDESELof the edit control, where this default arguably is the better choice. Incidentally, ListBox didn't have such an option at all, it would always show selection which couldn't be disabled. (exceptLBS_NOSELstyle which prevents any selection at all) – peterchen Sep 4 '12 at 8:17