Magnitude response and DFT normalization
There is no contradiction here. The first two points in your question are correct. In the third one the mistake lies in the assumption that "it represents the same system". It doesn't. You've shown yourself that the response to a sinusoid is different for the two systems; the output of the interpolated system is larger than the other one, which corresponds to the larger value of the magnitude response.

As a simple test, note that the value of the frequency response at $\omega=0$ is given by the sum of all samples (assuming a signal of length $N$):

$$X(0)=\sum_{n=0}^{N-1}x[n]\tag{1}$$

Clearly, this sum is different for the original signal and for the interpolated signal. Note, however, that for upsampling and interpolation by a factor of two, the difference is not necessarily a factor of two. The exact factor depends on the signal and on the type of interpolation.