Yes, because the constants that actually matter (fans, stadium, training ground, community) are kept the same, and football is about more than rules some suit-wearing FA bureaucrat made up. Siding against fellow supporters, dear me.
And the livelihoods of the people representing the small businesses that were shat on in the process?
They should be compensated by the necessary people. Unpaid debts and the continued existence of the institution Leeds United football club are not mutually exclusive. Because a football club exists as a group of fans who represent a community. And the Leeds United of 2012 is the same as the one of 2007, or 2005, or 1970, or 1919. I'd even say that it's the same as Leeds City who preceded LU's formation, since it was founded at the Hotel Metropole by influential LC fans, and followed by the same crowd. Just as I'd say AFC Wimbledon have a right to claim the history of Wimbledon FC, or FC United of Manchester with Man United, or FC Halifax Town with Halifax Town FC. Not with North London traitors Millwall, South London traitors Arsenal or plastic traitors MK Dons, who are true franchise clubs and have shamed themselves. There is no official fence marking the borders of Yorkshire or Lancashire or London, but everyone knows when they've arrived there.
It's nothing made up by suits and bureaucrats, it's simply the rules of the football league that clubs need to be members of. Leeds United gave up the right to play by disowning the so called 'golden share'. At that point the 'club' had no players or assets and was therefore incapable of keeping the position. A new club had been created and this club took over from the old one. This isn't the normal situation with clubs in admin when an owner buys a club with a place in the league. It's also different to AFC Wimbledon who did things properly and worked up the league ladder. It's just like MKFranchise who bought another clubs place in the league. Had they not done what you try to deride them for and bent the rules, that new club shouldn't have taken the place, an existing legitimate club should have filled the void left by the failure. Luckily for you, the football world took pity on Leeds and bent the rules to allow the new club to join the league in the space left by the failure. All that means that, as companies house confirm, Leeds was liquidated in 2008 and as the club argued in court, the new club has no links to the old one.
A certain gentleman from the City and County of Kingston upon Hull called Ebeneezer Cobb Morley codified the laws. Nothing to do with bureaucrats. You really don't know very much about Leeds, so it's no surprise you know less about football history. We're here to help you less fortunate types.