TL;DR: According to the Qur'an, ahadith, and fatawa, it's generally permissible to eat meat slaughtered by People of the Book provided we say the name of Allah over it, and provided the animal was slaughtered in an Islamically valid way. However, fatawa further state that the default assumption is that meat in the West is slaughtered in an invalid way, and not necessarily by People of the Book.
Food of People of the Book is permissible to eat:
According to the Qur'an, eating food of People of the Book permissible:
This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. ... -- Qur'an 5:5
And similarly there's a hadith:
Some people said, "O Allah's Messenger (ﷺ)! Meat is brought to us by some people and we are not sure whether the name of Allah has been mentioned on it or not (at the time of slaughtering the animals)." Allah's Messenger (ﷺ) said (to them), "Mention the name of Allah and eat it." -- Sahih al-Bukhari 2057 (sunnah.com) and variants Sahih al-Bukhari 5507 (sunnah.com) and Bulugh al-Maram [grade: hasan] (sunnah.com)
(See also the ahadith Sunan Ibn Majah [grade: sahih] (sunnah.com) [and Sahih Muslim 1930 a (sunnah.com)] and Sunan Abi Dawud 2817 [grade: hasan] (sunnah.com) which also express permissibility of eating meat of People of the Book.)
However, we need to keep in mind the importance that Allah's name be mentioned over this meat:
And do not eat of that upon which the name of Allah has not been mentioned, for indeed, it is grave disobedience. ... -- Qur'an 6:121
How meat is slaughtered matters:
The above were cited in an Islam Q&A fatwa, where they raise two conditions on the permissibility: (a) "the meat be slaughtered as a Muslim does it", and (b) "no name other than that of Allaah should be mentioned over it."
...if the companies or individuals who produce meat are people of the Book, Jews or Christians, and it is not known from them that they kill the animal by electric shock, strangling or striking it on the head, as is well known in the west, then this meat is halaal. ... But if they kill the animal by one of the methods mentioned, then the meat is haraam...
So the fatwa says that food in the West is widely known to be slaughtered in a way that violates the condition "the meat be slaughtered as a Muslim does it". Moreover, they write:
If those who produce the meat are not Jews or Christians, then the meat that they offer is haraam.
I suspect that Olive Garden, Pizza Hut, and the like, are irreligious organizations, so it's unclear whether or not their meat would be slaughtered by People of the Book.
Other fatawa also address both these points:
It is not lawful at all to place one self in a position of consuming haram or that which certainly doubtful. -- Mufti Abdurrahman ibn Yusuf, ZamZamAcademy.com, 2010
However, if the animal is not slaughtered according to the above method, or that the person who slaughtered it was neither a Muslim nor from the People of the Book, then the animal's meat takes the ruling of the meat of a dead animal and it is not lawful to eat it. -- IslamWeb.net, 2002
The meat that is sold in supermarkets and restaurants in countries with small Muslim populations, such as the United States, Canada, the United Kingdom, and other countries, does not generally meet the conditions of a valid Islamic slaughter and is not permissible to eat. -- Qibla.com, sourced from IslamQA.org