My experience of looking at the liquid limit and plasticity index of sub-base materials is it's there to provide an indication of how the material will behave (similar materials act in similar ways), and is the material likely to be frost susceptible. Experience has shown that where a sub-base has fines that are plastic, the material is more likely to be frost susceptible, even to the point of 'suggesting' that if the fines are plastic, its not worth spending the money on a frost heave test.
Going back to the point about the result of the LL being 27, and the limit being 25, I think this depends on whether you want to approve the material or not. If your experience suggests that this material is suitable, and there is evidence that this source has been succesfully used in the past, I don't think it should be a problem - subject to all other tests complying. There is an increasing interest in the 'degree of certainty' of measurement, what are the statistical confidence limits on the result? - not easy to determine but even taking a rough +/- 5% certainty on the result you get a rough range of 25.6 to 28.4. If there is statisitcal data available you should get a much better 'feel' for the range of the result. Also its worth looking at the repeatability and reproduciblity of the testing lab - again if its available. I am not sure of the QA system in India, but in the UK under the UKAS system, you have to be able to provide evidence of repeatability, reproduciblity and tracability of testing and equipment. Its not called in to question often, but on 'big' jobs where the cost implication can be massive it can be a very powerful tool to allow the identification of erroneous results.
If it was me, I would not worry about a single result, but would want to see the spread of results on a selection of samples, or at least the 'typical' range of results on the material over a suitable period of time. Similar to the way in which the new EN standards look at the typical property as opposed to singular values.
If on the other hand you don't think the material will be suitable - you can always argue that its failed so its no good, but somehow I get the feel you value your engineering judgment above conflicting arguements.
I would also like to make the point (I think I've posted this before) that from my own experience of doing the test, it is VERY difficult to get repeatable liquid limits on samples which are non-plastic - hence my suggestion of getting a spread of values and making an engineering decision, a single reading on this type of material would not, in my opinion, be sufficient to pass/fail the material source.