Good for you for questioning what some dubious black box computer programs are telling you!
Basically, an interdigital filter is made up of transmision line resonators. The clasic way of thinking of this is that each resonator has a static capacitance, and that there are mutual capacitances (or coupling factors) between the resonators. By chosing the static and mutual capacitances to coincide with a lowpass filter prototype design, you can get the desired response.
There is a pretty good description of this in section 10.06 of Matthaei, Young, and Jones' Microwave filters, impedance-matching networks, and coupling structures.