So, do you have anything 3ft high in the run that she jumps up on? Or can you make one? Does she look okay doing it?
Because the first thing fat should affect is a birds ability to get off the ground...
This particular hen has other complications besides, potentially, her weight, so she's not a good example of their use of heights in general... She has EYP and bumblefoot and avoids big jumps for that reason. Their roost in the coop is 4 feet tall, but they have two intermediate roosts spaced evenly between the floor and the top roost. All of the chickens use those to reach the highest roost, and all of them jump from the tallest one straight to the ground (thick pine shavings bedding). For some reason they don't want to go down incrementally. In the run, they have that "jungle gym" thing I built for them out of wide tree limbs (~6" diameter). The highest level is also about 4 feet, with 2 intermediate levels. All of the Orpingtons prefer the bottom level, some will occasionally use the middle level (the bird with the issues only uses the bottom), and only the Barnevelders will ever use the top level, and rarely. None of them seem to like climbing and heights, unless it's at night. On the rare occasion when I forgot to adjust the timer on their auto door for the growing days, and they got locked outside, every single one roosted on the top branch.
Does she even have experience with birds?
I doubt it.
Her lack of logical thinking, instead of 'knowing it all', would put me right off of her...
.....and I surely wouldn't do anything she says based on that.
She is one of the two vets in my area who will see chickens, and was recommended to me by a very good chicken-keeping friend of mine. But I have been very disappointed. Next time I need a vet, I'll try the second one and hope they are better... I don't have a lot of options though, most vets who even see birds only accept "standard pet birds" like parrots.
Get them out of the run and make them run.

Even an hour a day can make a difference if you ensure they keep moving and forage. I take the allotment chickens around the allotments and I herd them so they keep moving. Most of the time the opportunity to explore the next foraging opportunity keeps them on the go.
I'm in the suburbs, I don't have anywhere to let them run

I let them into my fenced-in garden during the off season to look for bugs, that's about all I can do.
She absolutely would not like one of my roosters then. He's at least 10lbs
APA standards for weight of a full grown rooster can vary a lot.
Well she was talking about hens, and hens don't weigh as much as roosters... But I agree, "hen" isn't any one single thing, and there is no one good number. She seems to only think of them in terms of "the big ones" (large fowl) and "the little ones" (bantam) and apply the same metrics to everything within those categories, which is just ignorant. Just between my two breeds of "big ones", the English Orps are probably at least twice the size of the Barnevelders, while being in the same category, so they can't be judged by the same metric...
Now, a lean (not muscular) high production layer of over 7 lbs might be considered obese, which might be where her knowledge stops.
That's my guess, too, that her experience is limited to production breeds, because a lot of recommendations and "chicken basics" out there come from the food industry standards on raising production chickens (for either eggs or meat).
Maybe try using plain food to get them to scratch around? Like take out the feeders and maybe in the morning they get “pretend it is scratch” food when they are likely quite hungry, and then the easy feeders show up later?
This is a very good idea, thanks! I'll try it.
If you take a rake or something and re-arrange the bedding without adding scratch, will they do just as much scratching? It might be worth trying.
They might spread it back out, not find enough goodies, and stop looking. Or they might find enough little bugs or whatever and keep scratching anyway.
They do like disturbed bedding, yeah, I can try raking/digging more often. Their bedding is a cold compost of various organic material - wood chips, dry leaves, yard waste, etc. and looks more interesting than a uniform generic bedding, like all sand, or all wood chips. There are things to find, and the chickens spend a good part of the day scratching around and digging craters regardless of whether I've thrown anything new in there. I feel bad that I am unable to let them out, but to compensate, I have put a lot of effort into giving them a large, varied and interesting run to hang out in.