Hi, I agree. No need to worry.
They will be full and fussy from free-ranging. They are too well fed.
My girls don't get into the scraps as much when they've been out.
If they needed it they'd eat it.
I bet they'd start to eat veggies if you grew them. I have to fence my garden off.
All I can add on veggies is, while I give my girls cooked veg if its left overs I don't cook it especially. I think cooking takes a lot of the goodness out and it's not natural.
Also chickens learn their behaviour and tastes by copying. Battery hens don't even know how to scratch or walk even if they have the strength. You can teach them to scratch by scratching your hand in front of them. You teach incubated chicks to drink by dipping their beaks in water. Either of those techniques may work with the watermelon. Ie 'peck' your finger at it or stick their beaks in it gently.
I haven't had chicks for years before these last ones recently. I watched them more closely and was fascinated to see how they learned. Every new food from grasshoppers to watermelon that I threw in with them was ignored until mum pecked it. Then stand back or you'd loose a finger. . With grasshoppers mum would grab it, incapacitate it and drop it in front of one of her babies.
With my next comment I will try not to offend anyone.
In Australia feeding meat and kitchen scraps containing meat (called swill) to livestock, and that means our chickens, is banned. It has been linked to the spread and cross over of disease between species in other countries. I know a lot of people do it but I don't. My livelihood has depended on our country staying disease free.
My girls only get veggie and fruit scraps. They get their protein from other sources.
1. Worms and grubs from free ranging - and the more they free range the more earth worms there are for the garden.
2. Laying mash. It should be a good balance of all they 'need'. If you are buying the mash from Northside Produce I think it is a bit low in protein. 16%. It was not enough for my pullets at 40wks to start laying. When I increased the protein I got eggs in days. There are different opinions about how much protein they need and it changes - winter, moulting etc. But for laying I think 18% minimum.
3. Protein additives - You will have seen my other posts about the soy meal I have been using of late. So far I love it to bump that mash up from 16%.
Finally, and I know I've given you more than you asked for, it is important to remember that every treat you add to their diet you are detracting from the crucial elements of a balanced diet.
I hope this helps and isn't an overload.
Cheers