If you read enough on the internet, you’ll find lots of conflicting opinions about just about everything. If you think you’ve got a good veterinarian, that’s the opinion I would trust the most because he or she knows your horse and your environment. If your vet thinks limited pasture is ok, that’s what I would do.
From your description, it seems Charlie had a fairly mild case of laminitis and he just needs to lose some weight and go easy on the grass. My horse had a pretty significant laminitis attack and x-rays showed gas pockets in his hooves while he was recovering. Those had to grow out completely before I could ride him again, and that took several months. He was also about 200 pounds overweight, and it took a couple of years to get that off him. My poor guy was frustrated at being confined and restricted from all that lush grass, but he lived through it. Even through all of this, he was never completely off the grass. At first I just hand grazed him a few minutes each day. As he healed, I started to let him out in a small paddock to graze and I gradually enlarged his paddock using corral panels and allowed him gradually more time on the grass, always muzzled. My point is, if your vet says limited pasture is ok, it probably is ok. Charlie will be happier if he gets to graze, even if it’s only a little.