TLDR: Scroll to the end of the post.
The source of the problem is that what trumpet players call "pedal tones" depend on how "pedal tones" are defined.
Pedal tones on most brass instruments are usually defined as the fundamental pitch....
Trumpets are a slightly different animal, though. First, the design of the trumpet has an acoustical impedance that makes their “pedal C” below the treble clef staff not quite function acoustically quite the same way it does on the other brass. Furthermore, trumpet players usually talk about the pitches between low F# and pedal C also as “pedal tones.” In contrast, other brass players tend to call those “fake tones.” (SOURCE)
Confusion arises from whether "pedal tone" is taken to be synonymous with "fundamental pitch" or whether it means "fundamental pitch, also natural to the instrument."
The pitches trumpet players call "pedal tones" -- the pitches from the F below the lowest F#, descending to the C below (written) middle C -- are the instrument's fundamental pitches, but they are not natural to the instrument. By contrast, on tuba and trombone, the pedal tones (fundamental pitches) are a naturally occurring sound.
Certain low brass instruments such as trombone, tuba, euphonium, and alto horn are whole-tube and can play the fundamental tone of each harmonic series with relative ease. (SOURCE)
The previous article continues:
the fundamental is chromatically discontinuous with the lowest 2nd harmonic reachable on a three-valve instrument or via the seven-position slide on a trombone. Trombone and tuba in particular are often called upon to play pedal tones and "false tones" or "privileged tones" which have a pitch between the normal range and the fundamental.
Where tubas and trombones differ from trumpets is that the trumpet's fundamental pitches are not discontinuous from the normal range of the instrument. One can play "trumpet pedal tones" from C to F and then continue into the instrument's normal range with F#. On the other hand, low brass pedal tones "sound good", whereas the trumpet's "pedal tones" are a clearly different timbre than the rest of its range.
The key to all of this lies in differences in the instruments' construction: specifically, the width and "conical-ness" of the bore. "Whole tube" instruments (see above) have a larger bore, which is what allows for the production of a "true" pedal tone. This is in contract to "half tube" instruments, which have a narrower bore.
Whole-Tube Instrument – a brass instrument capable of playing its fundamental pitch (the so-called pedal tone).
Half-Tube Instrument – a brass instrument that cannot play its fundamental pitch.
What makes an instrument whole- or half- tube? There are two factors. One is how wide the bore is.... The second factor is how conical the bore of the instrument is.(SOURCE)
(Note that the above article goes on to say that "whole-" and "half-tube" are messy concepts, and it's better to look at the actual capability of the instrument.)
Thus, low brass are capable of both "pedal tones" (fundamental) and "false tones" (between the fundamental and second harmonic); trumpets can play the fundamental, but those pitches more resemble what are called "false tones" on low brass.