I bumped into a question concerning the place where the "really" should be.
I get confused because Google seems to have more results for "it can be really exciting", so I wonder which one is correct.
The differences here lies in emphasis. In the case of "can be really exciting", really modifies exciting. In the case of "can really be exciting" (which is equivalent to "really can be exciting"), really modifies be. The first case assumes that something is exciting and emphasizes how exciting it is, whereas the second case emphasizes the fact that something could be exciting in the first place, without assuming it.
The use of the word 'really' in this context is informal, even casual. It adds nothing to the word 'exciting', beyond the mood or attitude of the speaker. It is an example (stylistically) of a kind of inflation. No adjective is strong enough: 'exciting', 'thrilling' are already virtual superlatives, replacing words like 'fun', 'amusing', 'interesting'. It is a common, I should add 'unfortunate' habit to replace the positive with some kind of superlative. What it actually does is devalue the positive, as all inflation devalues.
For all that, it is how people tend to communicate on facebook, in the coffee house and elsewhere. It even creeps into official English. For example, Ofsted replaced 'very good' (already a superlative(-ish) term, with 'outstanding', which ought to be a descriptor for what is rare.
My reason for this answer is to point out that what we have in the difference between 'being really exciting' and 'really being exciting' is not the result of deliberate thought. So there is no point searching for subtle distinctions of meaning or even grammar. The injection of the (in effect) redundant 'really' is more like a particle, reflecting the speaker's state of mind. In fact, it could be argued that it is a sort of 'particle', a phenomenon so common in ancient Greek that whole books are published on the subject, such as "The Greek Particles" by D.L.. Denniston. For example, the particle 'ara' (αρα) could be used either to tell the listener/reader that they he is reading a question or to indicate a quizzical or skeptical attitude to what is being said/written.
You can tell that this is how 'really', used in the question, is like this, try negating it. 1. "No, it is not really exciting". Or 2. "No, it is really not exciting". In these cases, there is, in fact a more marked difference. Both mean not that it is not exciting, but might be quite fun. It means that either 1. it is a bit dull or 2. it is dead boring.
So this use of 'really' is certainly well-established in English usage. But it is not to be recommended to speak or writing that seeks any kind of precision.