... so I am telling a lie when I say 'x', when I could have more accurately said 'x', but please note that 'x' includes or excludes 'y'.
I doubt many of us add all the additional caveats and 'small print' that you seem to be expecting which means we are all lying loads of the time.
So lets address the current case:
Headteachers are protesting over school funding cuts
Government claims school funding is at record levels
How do we square the circle:
Well because the Headteachers are talking about real-terms per pupil funding, while the Government is talking about total cash funding.
Point being in your example unless the Heads make is clear that they are talking about real-terms per pupil funding and not cash funding levels then they are lying. Unless the government makes it clear that they are talking about cash funding levels and not real-terms per pupil funding then they are lying.
In my view neither are lying, both are making correct claims but ones that open to interpretation - of course I am with the Heads, as it is real-terms per pupil funding that is important, but unless they are absolutely clear in stating that, by your interpretation the Heads are lying.