When dealing with big companies, you always have to account for the fact that they do not stand for principles, consistency or 'artistic integrity'. They stand for the Almighty Dollar. It's the one thing they care the most about. Whatever makes the most amount of profit for them is what they want, regardless of anything else. If going out and destroying every copy of every Alien movie in the world would make them more money(and was legal), they'd do it rather than leaving them out there. Of course it wouldn't, since having a movie out there making money on DVD/Blu-Ray is better than investing all that money in a film and having it not be out there.
So why do I think that Fox is going to let Bloomkamp do what he wants to do with the Alien universe, up to and including acting as if Alien 3 and Alien: Resurrection never happened? First, it seems as if Fox is more eager for Bloomkamp to work on an Alien film than he is himself. Bloomkamp has said "I'm the problem. Fox, they would make it. Like, tomorrow. They would make it,". 'It", at the time, referring to whatever actual treatment that he had made to go with the concept art he released in January. So Fox is on board with what Bloomkamp wants to do, and are doubtlessly willing to accommodate to a solid portion of his desires as a filmmaker. Otherwise, he'll just walk away. He's shown a contempt for the studio system, particularly large franchises after the whole Halo movie snafu. So the studio has to make the movie pretty much as he wants to, or he walks. And they really want him to make the movie. So the wheels already seem to be in motion for A3 and A:R to be ignored in the upcoming Alien 5.
The reason Fox is going that direction HAS to be because they think the movie Bloomkamp wants to make will bring in more profit for Fox than not making one at all or making one without Bloomkamp. The reasons for Fox thinking this, from my POV, are as follows.
1. Alien 5 has been in development hell for so long, if they don't make it soon the entire franchise will continue to stagnate a'la Ghostbusters, and stagnation is not good for a film franchise's profits.
2. Neill Bloomkamp is pretty much the last legitimate sci-fi director who's willing to even touch this franchise. Given what the series turned into, who can blame Ridley Scott for going his own way with Prometheus and Jim Cameron not even touching the franchise in two decades? The fact that a popular, experienced, critically acclaimed sci-fi director is willing and able to make a new Alien film is something that the Fox suits cannot afford to ignore if they want the franchise to continue to make them money. This is a big chance to bring the franchise back to profitability which they can't ignore.
3. Alien 3 and A:R will make more money if Alien 5 is made than if Alien 5 isn't made, regardless of whether or not it is a success or if it ignores A3 or A:R. It's simple fact that when a new film in a franchise is made, the previous movies make more money through home video. If no Alien 5 is made, A3 and A:R will just continue on in $25 boxed sets, $10 special/elite/director's cut/SUPER-EXTENDED-UBER! Editions and $5 vanilla copies at Wal-Mart rather than making any extended boost in sales or profitability. Even if Alien 5 fails at making money, more people will be curious about the previous Alien films than before if through name recognition than anything else. New fans will be brought in, old fans will be rejuvenated in their enthusiasm for the brand. All around, a new movie is a good thing for previous installments, regardless of how the new movie itself does.
4. They figure that more fans will be gained through Bloomkamp's Alien 5 than will be lost. I think, and feel free to correct me if I'm wrong, that the people who think that that last two Alien films(or at least the third one) are better than the first two films are in the distinct minority in the Alien fanbase. Especially when you include all the people that are fringe fans and/or don't have the kind of dedication to the Alien world that people who join this site, for instance, have. Every new film in a franchise brings in more people who never saw any of the previous films. I know it might shock us all, but for some people, Alien: Resurrection was their first exposure to the franchise. As horrible as that may be to comprehend, it's true. I remember seeing a trailer for A:R before I'd ever heard of the first three films. I was only 10 at the time, but it's my first memory of seeing anything like that kind of science fiction. Up till then, it had all been Star Wars/Trek. After I saw that trailer and heard it was part of a franchise, I was curious and as soon as I saw the first movie, I was hooked. They gained a lifelong Alien fan(not to mention the money that comes along with that) just through the trailer of what is almost uniformly considered the least of the Alien films. The same thing can happen with Alien 5, even if it tanks. And if it becomes a success, the effect will be multiplied far greater than the number of fans that will actually refuse to see Alien 5 due to their love of Alien 3/Alien: Resurrection. It's the numbers of the game.
So again, no matter how dear A3 may be to some of us, the reality of it is that Fox doesn't care about that. Really, it barely even factors into their thought processes. They're all about the money. Individual directors and producers and even some executives can be otherwise, but for the company as a whole, it all comes down to profit. And as long as we're dealing with Hollywood, that's the way it's going to be.