  An analysis of recent experimental data [J. Khuyagbaatar et al., Phys. Rev. C
104, L031303 (2021)] has established the existence of two fissioning states in
$^{253}$Rf: the ground state and a low-lying isomeric state, most likely
involving the same neutron single-particle configurations as in the lighter
isotone $^{251}$No. The ratio of fission half-lives measured in $^{253}$Rf was
used to predict the fission properties of the 1/2$^{+}$ isomeric state in
$^{251}$No and draw conclusions as to the stability against fission of even
lighter Rf systems. This paper focusses again on the fission properties of
$^{253}$Rf and their impact on the stability of other neutron deficient
isotopes, using new and improved data collected from two experiments performed
at the Flerov Laboratory of Nuclear Reactions in Dubna, Russia. Two fission
activities with half-lives of 52.8(4.4)$~\mu$s and 9.9(1.2) ms were measured in
the case of $^{253}$Rf, confirming the results of J. Kkuyagbaatar et al. A
third state, at much higher excitation energy, was also observed through the
detection of its electromagnetic decay to the 52.8$~\mu$s state. This
observation leads to the opposite quantum-configuration assignments for the
fissioning states as compared to the ones established by J. Khuyagbaatar et
al., namely that the higher-spin state has the shortest fission half-life. This
inversion of the ratio of fission hindrances between the low and high-spin
states is corroborated in the isotone $^{251}$No by the non observation of any
substantial fission branch from the low-spin isomer.
