Some great points here. If someone is a music student at the college level, they learn piano and I think that is obviously great. They don't ask the internet - it is part of their curriculum.
I think the advice here isn't for full time music students or even full time musicians.
A bird watcher doesn't need to be a bird to identify birds. If the chords are in the air, at some level it doesn't matter who is playing them. If you play tunes with people and have a chord chart and any sort of ear, you end up knowing what the chords sound like.
It takes a lot of work to get good bass lines going that are in time and in tune, dealing with the root movement, fifths, leading tones and chromatics. My suspicion here is that we primarily speaking to bassists who are not doing that at a very high level thinking piano is the answer and I just don't think it is.
To your point, if you want to be a "featured soloist" you are probably going to need both the virtuosity and the piano skills - the upper harmony is going to be far more important to your work.
If not, you are far better off getting the root movement solid and in tune.
A big difference between piano and guitar, is piano allows you to play chord inversions and smooth voice leading relatively easily. It's also much easier to visualize the chords and voice leading on piano. To me this makes a huge distinction in how you hear things. Guitar tends to result in a lot of parallel voice leading unless you are really, really good. From what I have observed, you have to plan out what your are doing in order to achieve relatively smooth voice leading on guitar.
To me the biggest advantage guitar has over piano is convenience/portability.
For the record I currently own a guitar and have not owned a keyboard for years. I am also often frequently frustrated by the inherent limitations and challenges of the guitar. IMHO the piano opens up a far wider horizon of harmonic possibilities than guitar, and also gives you a much more clear, direct, and linear visual process for understanding any concepts you are studying.
I find the tuning of the guitar both a blessing and a curse. I use standard guitar tuning and my primary BG is a 6-string tuned in 4ths. When I play guitar more it tends to reduce my reliance on finger patterns on bass, so my soloing becomes less mechanical.
However I have struggled to truly memorize the guitar fretboard and I find playing guitar confounds my conscious knowledge of my bass's fretboard. My conscious mind can't really seem to keep the two instruments separate. My fingers don't seem to have as much trouble though, as I seem to be able to rely on my ears to play the proper notes.
So I think either instrument can help one become a better bass player. I think guitar has specifically opened up my mind to more melodic ideas by interrupting my normal thought processes so I can play bit a more freely on bass.
But I think piano is far more efficient for ear training and learning music theory. It takes you beyond mere mastery of the bass, and it is unlikely to confound your knowledge of the bass.