The point why a simulation must not deviate too much from the real game is due to the following reasoning. You assume you have an adversary that wins the original game, but you do not know how the adversary acts if you deviate from the behaviour of the real game and the adversary can notice this. Exactly because you make no assumption whatsoever about the adversaries behaviour when encountering a behaviour in the simulation that is not covered by the real game. If the adversary can now always force your simulation to deviate from the real game, then you cannot use the adversary anymore as you cannot predicts its behaviour anymore (e.g., you simply have to abort the simulation every time since you cannot answer queries of the adversary and you do not know what the adversary does if you can not answer a query).
If your simulation fails with a probability that is non-negligible, then this is not a problem per se. What you need is to estimate the probability that an adversary causes a simulation to fail. Typically, proofs try to somehow partition the set of potential queries into those that are answerable and those that force the simulation to abort. For instance, assume that this partition is randomly defined according to some distribution and the simulation does not leak any information on which queries would be bad, then the adversary has no better strategy than "accidentially hitting" a query in the wrong partition and you can easily estimate its probability (as it is independent of the adversaries behaviour).
For instance assume you as a simulation have to guess that the adversary does not query 1 in $n$ possible things, because you cannot answer this one query. Think for instance (i.e,. you have partitioned such that you have $n-1$ queries that are good and 1 bad query). Now, if you randomly choose $i\in [n]$, then the adversary has no better strategy than accidentially hitting $i$ (i.e., the simulation is exactly as in the real game except the unwanted event happens and let us assume that this event is independent from the other things the adversary sees in the simulation). Then for every query the probability of an abort is $1/n$ and if the adversary makes a polynomial number of queries you just loose tightness in the reduction (you condition on the event that the adversary does not hit bad in all queries). Now, the simulation will always abort with the same probability irrespective of the adversaries strategy and you are fine. A nice brief discussion on how to formally model this can be found in Alex Dent's A Note On Game-Hopping Proofs. But actually the reasoning and the calculations are very simple. Note that also here there is a difference in the behaviour of the oracle in the real and simulated game and this does not mean that the proof does not make a sense.
However, if any adversary can always force the simulation to abort, then you have a problem. The problem as with Waters proof is that the probability of the adversary causing an abort of the simulation is not independent of the adversaries behaviour (as above). So he cannot relate the winning probability of the adversary and the reduction meaningfulle. Thus, he has to introduce this complicated artificial abort technique. As you already mention, can be avoided when using the strategy of Bellare and Ristenpart.
If you have a problem with a specific proof it may be easier to ask a specific question. I am not sure if my edit helps you.
