One thought experiment which shows that a quantum theory of gravity needs a background is described here:
http://arxiv.org/abs/0909.1408 To understand this, you need some basic understanding of the double slit experiment: You see an interference pattern if the slit remains unknown, but, if you measure which slit is used by the particle, the interference pattern disappears. To measure the position, you can, in principle, use the gravitational field of the particle, and test it with some test particle. If the influence of the gravitational field is strong enough to make a difference, the position is measured, and no interference picture appears. If not, the test particle will be on the same place independent on the slit used by the particle, thus, measuring the position of the test particle does not tell us anything about which slit was used. Now we translate this to the language of quantum gravity, with a superposition of the gravitational fields. If a massive particle goes through different slits, the gravitational fields will be different. We have the trajectories of the test particle in the two gravitational fields. Then, we can measure if there is an interference picture. If not, then the test particle is at the same place. So, we can measure if the particle is at the same place, for different gravitational fields. But this is impossible if there is no preferred background. In this case, you have two solutions, and the point where the test particle is, on above solutions. But there is no way to tell which point on one solution is the same point as one on the other solution. You cannot simply identify the same point on above solutions by having the same coordinates, because you can change the coordinates on above solutions independently.
This may be too complicate for you, but this consideration shows me that there cannot be any quantum theory of gravity without this additional background. This problem of quantum gravity has nothing to do with the SM, which is already a quantum theory, and which has a fixed background, at least all what we need from a fixed background for this problem, namely the Minkowski space.
The other point where the hidden background is necessary is the violation of Bell's inequality. There is Reichenbach's common cause principle: Every correlation has a causal explanation, and a correlation between A and B can have three causal explanations: A->B, B->A, and some common cause C with C->A, C->B. Now, the violation of Bell's inequality allows to exclude a common cause. So, two explanations remain, A->B or B->A. Above require faster than light hidden causal influences. Then, the preferred (and similarly hidden) preferred time is the time coordinate with the property that if t(A)>t(B) then A->B is forbidden - there is no causal influence into the past. The alternative here is to give up causality, Reichenbach's common cause principle, and, as a consequence, the search for causal explanations of observed correlations.
What is missed in the SM is an explanation why we have the fields which we have. The SM postulates them, without giving any explanation. But the explanation I have found does not have a relativistic symmetry on its fundamental level, this symmetry appears only in the large distance, continuous approximation. But if relativistic symmetry is only an approximation, the fundamental theory gets a preferred frame almost automatically.