The choice of a capacitor in parallel with a battery depends on the capacitor having a lower impedance than the battery.
I think there may be semantic differences in describing voltage noise.
Inductance can cause voltage spikes with rapid chanes in current, and a capacaitor with low ESR, low SRF value will help greatly reduce by the spike current that it can suppress with A lower ESR than the battery, where dv=Ic*dt/C , but generally we refer to
ripple as the fundamental noise frequency after the spikes are suppressed.
In fact the equivalent passive equivalent circuit of the capacitor is the same model as the battery.
The series resistance, R1 of a lead acid battery tends to be much lower than a capacitor. But
when connected to long inductive or resistive leads, thus capacitors should be located closest to the load, is used are more effective than directly across the battery.
When it is battery ESR issue, the capacitor should be closest to the battery.
But if the load path length is short with very little inductance, the ripple may be reduced without any benefit from a capacitor. Thus it is the wire inductance that needs the filter more than the battery. However , short proximity may not be possible, so adding a low ESR is suggested.
Consider a flooded 12V lead acid with 100A ripple current causing 1V ripple voltage. Thus given ESR = 1V/100A=0.01 at 50 Hz. , where dt= 0.01s. To reduce the V-ripple to 0.1V would require an ESR of 0.001 and a capacitance of C=Ic*dt/dv=100A*0.01s/0.1V=
C=10 Farads