CT secondary should not be kept open

True. The secondary of a current transformer must never be left open while the primary carries current. It should be short-circuited (or connected to a low-impedance burden) first.

Justification

In a CT the primary is in series with the line, so the primary current $I_1$ is fixed by the load of the power system and does not depend on the secondary. Under normal working, the secondary current $I_2$ produces an mmf $N_2I_2$ that almost cancels the primary mmf $N_1I_1$. Only a small net mmf (equal to the exciting mmf $N_1I_0$) remains to magnetise the core, so the flux is small.

If the secondary is opened:

1. $I_2 = 0$, so there is no opposing mmf. The full primary mmf $N_1I_1$ acts as magnetising mmf.
2. The core flux rises sharply and the core saturates deeply.
3. The secondary has a very large number of turns. The emf $e_2 = N_2\,d\phi/dt$ becomes a high peaky voltage (several kV), which can break down the insulation and is dangerous to the operator.
4. Core loss rises greatly, so the core overheats and may be damaged.
5. A large residual flux is left in the core after the primary is de-energised, which spoils the ratio accuracy of the CT.

Hence the statement is true.