Actually, Charlie measures not the qubits themself, but the result of its interference.
As there are currently no reliable quantum information medium other than photons, lets speak about photons:
- Alice prepares photon $a$
- Bob prepares photon $b$
- They send this photons to Charlie
- Inside the Charlie's setup the photons interfere and Charlie measures only the result of the interference.
The qubits are prepared in bases, so Charlie can't reliably measure them (he will chose the wrong basis with 50% probability).
The result of the interference does not have any correlations with individual qubits.
Meanwhile, for those, who exactly knows one of the qubit states, interference unambiguously points to the state of another qubit.
A classical analogy:
Imagine, Alice and Bob send classical bits $a'$ and $b'$ to Charlie, but for some reason it is impossible to measure them directly. Charlie is only able to measure $c = a'$ XOR $b'$.
Alice knows $a'$ and $c$, so she can find $b'$.
Bob knows $b'$ and $c$, so he can find $c'$.
Charlie knows only $c$, so he can't cfind neither $a'$, not $b'$.