filters - Minimum Sampling Rate of Bandpass signal

Consider a DSBSC signal s(t) = m(t).cos(2.pi.20k.t) where say m(t) is multi-tone signal with frequencies less than 5 kHz.

The spectrum gives a typical bandpass say triangle centred around 20k and -20k. Now, when I calculate the minimum sampling rate;

Since the highest frequency is not an integer multiple of bandwidth of the bandpass signal; I end up getting the sampling rate as 25 KHz.

But when I draw the spectrum for the sampling rate of 10 kHz, the message signal centred at origin was doubled in amplitude and there was no aliasing as well.

Does that mean the minimum sampling rate is indeed 10 kHz?

I have used the typical bandpass sampling rate procedure many times, this was the first time it failed in giving me the minimum sampling rate!

edit: I doubt that the 10 kHz would be the minimum sampling rate to recover the message signal while the bandpass sampling rate of 25 kHz is the one which recovers the bandpass spectrum!

Also, if the above conclusion is correct, is it independent of the carrier frequency (Fc>>Fm)?