Salad greens are mostly water and nutrients, so nothing to get fat on. Would we get fat on eating a plain salad of greens every day? Nope. So the same applies to rabbits. Now, if we're talking about other health issues and not weight gain, high calcium/oxalate greens can certainly cause some health issues for some rabbits, so that is always a consideration when deciding what greens to feed and how to feed a good balance.
And if this is to include forage like Preitler mentions, there are plants that are high in protein, like alfalfa or early growth grass, etc, and higher protein forage could cause weight gain if these high protein plants were fed exclusively or in excess, without much variety of other lower protein higher fiber plants to balance them out. But then, you would also be likely to encounter other health issues from feeding an excess of these high protein plants as well.
So if this person is specifically referring to salad greens in their argument, they have science itself proving their claims false. Which should be enough to convince anyone, even the claimant themselves, of the inaccuracy of their statement. But then some people are determined to stick their ground, even with science proving them wrong.
If this person is claiming these things based on studies, then they should be producing the links to back up their statements. Otherwise it's just talk. Just as is their claim that rabbits on a pellet diet don't get GI stasis. Every rabbit is prone to GI stasis, no matter the diet, as there are a variety of health issues that can cause it, not just diet. But a lower fiber, higher carb diet(like found in a high pellet diet, particularly lower quality pellets) most certainly can make a rabbit more prone to developing GI stasis. There are plenty of owner accounts that could prove the statement false, if you want to further look into it.
Just my own experience can prove this statement false. I had a new rabbit on an exclusively pellet diet with hay for 'enrichment'(which he didn't eat) and no greens, when I got him. He kept getting GI stasis(still on the previous diet he came to me with), back to back. That's when I discovered it was the pellets from him consistently acting uncomfortable(eg belly pressing, kept shifting position, eye squinting, lack of appetite) just after eating his pellets. Once the pellets were removed from his diet and he was put on a hay and select leafy greens diet, he never had GI stasis again(he had a specific sensitivity to something in pellets).
Gut motility in rabbits, and reducing gi stasis risk, has everything to do with fiber, which is what drives a rabbits digestive function. Look at the fecal balls of rabbits on low fiber diets(usually high pellet, low hay diets) and high fiber diets(usually low pellet, high hay diets). Fecal balls are much larger the more indigestible fiber a rabbit gets, which is evidence of better GI motility. But don't take my word for it. You can research how a rabbits digestive tract works.
https://www.vettimes.co.uk/app/uplo...nd-function-of-its-gastrointestinal-tract.pdf
https://rabbitwelfare.co.uk/wp-content/uploads/2013/05/article-ROWinter10p7.pdf
http://www.therabbithouse.com/diet/rabbit-digestive-system.asp
https://rabbit.org/journal/3-7/gi.html
https://rabbitwelfare.co.uk/rabbit-health/illness/gut-slowdown/
(LINK CONTAINS GRAPHIC MEDICAL RELATED PHOTOS)
In depth rabbit history and biology:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7158370/
The internet is full of so called 'experts'. And claiming to be a vet, or even really being one, doesn't make someone an expert, or at all knowledgeable about rabbits. There are plenty of vets out there that know very little about the proper care of rabbits. And just as Preitler said, just because someone says something with certainty doesn't make it true. The link Preitler shared, it's a good one and one I would trust, as that vet actually is a rabbit expert(based on her multiple qualifications and decades of experience with rabbits), and was one of the best rabbit specialists in the world until she retired.
When I decide what info to rely on, I go off of my own experience and what I've learned from having many pet rabbits over many years, from verified research and studies that I've actually read and looked into(not just told about by others as being 'true'), from reputable and long established rabbit sites with decades of experience with rabbits(eg. hrs, medirabbit, rwaf, etc, but even then I research their info and claims), as well as the collective experience and stories from other rabbit owners and particularly ones that have proven to have reliable info from years of their own experience with rabbits.
I use all this combined knowledge and info to guide me about what things are good for rabbits and work best for them. I never just take someones word for it. I research and look into things that I feel are important points, and make my own determinations from what I find, as best I can. Never just trust what one individual is claiming, even me, without your own research and experience to discover what the reality or truth is. Everyone has an opinion, but that doesn't make it true or accurate.
and they love to have their own garden in the summer. 
