Minimum Sampling Rate of Bandpass signal
The problem is that the general criterion for bandpass sampling (which results in $25\text{ kHz}\leq f_s\leq 30\text{ kHz}$) applies for general signals, whose spectrum may not be symmetric around $f_c$. In your example, sampling at 10 kHz would fail because spectrums of different shapes overlap.

The most complete resource I know on bandpass sampling is "The theory of bandpass sampling", by Vaughan et al, IEEE Trans. on Signal Processing, 1991, Vol. 39, Issue 9 (http://dx.doi.org/10.1109%2F78.134430). At the start of page 4, it specifies that in the special case of DSB signals, the minimum sampling interval is $1/B$, where $B$ is the bandwidth (for both sidebands). This corresponds to your case, where the minimum sampling rate is 10 kHz, equal to the signal's bandwidth.