Eating halal food

I agree with your point here. If something is not there then its not there. If someone likes to add by making some connection its their prerogative. Nothing to do with religion.

Having said that, people exercise caution based on doubt how the meat was obtained by someone else.

There are people who do not eat meat even at muslims house bought from a halal/zabiha shop, unless they know if the meat was bought from a certain specific shop which they think sells correct zabiha meat.