There's a lot things that may be going on here. First of all, I have to note that I am neither a biologist nor a bioacoustics expert so I will just try to provide my view here in case it can help.
I can't find a connection of the curves of equal loudness (as the Fletcher-Munson curves are also termed) to your problem. These are related to the response of the human hearing system/mechanism to "simple" (co)sinusoidal excitation (this is how originally the curves were created although refinements and newer results may have altered or even confirmed their validity with other signals too).
The curves connect the objective sound parameters (amplitude and frequency) to the subjective feeling of loudness. In contrast, your problem, in my opinion, is of pure objective measures.
Increased bandwidth with increased amplitude
I believe that in order to reach the conclusion that higher amplitudes result in higher frequency bandwidths at the source (this is the frog) you have to perform some measurements at the source, which of course is these other species. In any other case you can't really say whether increased volume results in higher bandwidth.
From my limited knowledge on human voice (I am completely ignorant to bioacoustics and I will use human voice to make my point), the way to increase your bandwidth is not through the volume. At least to an approximation, human voice is modelled as a linear system (an example is a pipe with non-constant diameter excited by some wide-band signal from the vocal tracts) which, due to its nature (linear) cannot introduce frequencies that do not exist in the excitation.
I do know of specific case where the person deliberately can change the frequency spectrum of their voice but most often this is a result of training and not something common. Of course, this may not be the case in the frog species of interest.
Finally, there may be some non-linear effects taking place in the vocal generation mechanism of the frogs, or other species of interest. These may well introduce additional frequencies in the spectra with increasing volume.
Possible explanation in the linear case
Although you may very well argue that the data (the spectrograms and your detector) show evidence of extension in the bandwidth of various species with increasing vocalisation volume, there is still a possibility that the extension is not present.
Assuming that the species that are not of interest do have energy in the band of interest (the band where the frog vocalisation is most prominent, $5.5 ~ kHz - 7.2 ~ kHz$ according to your data), when their volume is increased, the spectrum will just rise in a "kind-of" linear way (this is rarely the case in my limited experience) with all frequencies rising pretty much equally.
If the energy in the band of interest exceeds the threshold of your detector (here I assume you are using some kind of energy detector) then it could be triggered providing a false positive.
In the case of your spectrograms, it very well depends on the parameters set on the plotting algorithm. Blanking may be used for very low values, or even logarithmic scale, or non-linear logarithmic scaling (this could range from using logarithms of different bases for different value ranges, to applying scaling - like blanking - after the conversion to the logarithmic scale), or any other set of parameters that do are not appropriate for the data at hand could very well hide the energy in this band up until it starts to become significant.
This is one of the reasons I stated that, in my opinion, you should measure the interfering sounds at different volumes to see whether there is indeed energy in the band of interest irrespective of the volume or there is indeed some mechanism in the voicing of the species that results in bandwidth extension. Nevertheless, this could very well be the topic of a completely different project out of scope of the one you are working on at the moment.