I'm almost suspecting that they might be worried, not just about treating the host as a cookie, but that people might be playing with, or desecrating the host. People playing vampire-hunter RPGs, or messing around with 'magic', etc. In a small congregation, the priest would know the regular parishioners, and who was eligible to take Communion. In a large congregation, or a well-known church, less likely.
On our family's brief foray into church-going, that was one thing my parents specifically warned me and my sister about: we were NOT to go up front when everyone else did. And my mother shot my father a dirty look that said "And don't even think it would be funny to encourage them to go!" Neither of my parents went, either, but that was more of a matter of principle, I think.