No, it isn’t, you are thinking about aliasing which is a key part of the sample theorem… however it only holds true for an impulse stream … … therefore the sample theory states that only a series of values that represent infinitely small durations of time with infinite power can be totally accurately reconstructed (an impulse stream) … obviously this is physically impossible… and only possible in mathematically pure constructs.
The reconstruction filter is about mitigating these approximations along with the ‘zeroth-order hold’ technique for physical implementations.
If you are interested I can point you to some good DSP engineering and scientific texts that can take you through this without being too heavy on the maths…remember mathematical absolute models can’t usually be realised in reality… and our sample theorem is a classic case of this that one can learn about in DSP engineering.
Chapter 3 explains exactly this.
I found Dr Steven W Smith’s book invaluable on DSP design and explanation… and I still have a hardback copy in my study…