The issue is whether your parents intent to temporarily stay or plan to immigrate. If they plan to immigrant, then a form I-360 should be filed by the petitioning religious organization. If they have a child who is a U.S. Citizen in the U.S.,then the consular official reviewing the R-1 and R-2 visa petition may be a bit more strict.
Since most attorneys don't claim to have extra sensory perception, we cannot determine what a consular official will be satisfied with as a matter of discretion. What we do encourage clients to do is not to lie.
The above is general information, not legal advice, and does not create an attorney-client relationship.