Is it permissible to eat from a restaurant owned by a Muslim in non-Islamic countries that sells meat regarding which one is unsure of the method of slaughter, given the availability of ritually slaughtered meat at home, and is this considered scrupulousness or piety?

If the restaurant owner is a Muslim and refrains from selling forbidden items, then the default assumption is that imported meat is permissible (halal), and it is permissible to eat from it unless there is something that raises doubt. When in doubt, one must investigate and take precautions to dispel uncertainty. As for someone who finds nothing to doubt, it is not permissible for him to harbor ill suspicions or to search for matters that have no evidence.