I've been to the vet on 3 seperate occasions to have grass seeds removed from inbetween my dogs toes.Believe me!Now i check every orifice of my dogs if we have been around areas where those seeds are everywhere.My experience with them are that they are very painful/uncomfortable for the dogs and they wont stop licking at the site until the seed is removed.
TBH i would be too scared to leave a seed inside my dog to migrate to goodness knows where,but in your case it sounds as iff the seed has travelled to far for the vet to simply pull it out with forceps,as was done with my dogs.And an operation

to remove it could be in order :(
A friend of mines dog got one stuck up inside his nostril,the vet couldnt remove it and somehow he ended up sneezing it out after a couple of days(of nearly constant rubbing and sneezing).
All i can advise is to check inbetween your dogs toes and other areas where they can lodge after each walk,it only takes a minute or so and is well worth it when you find some and easily pull them out from their fur,which i have done on numerous occasions!
I dont know what you should do with your current dog..maybe get another opinion?? Because as i said i would be worried about where the little sucker could be travelling to.