You are right. But there is more than you think if you please read my Arabic article here:
http://www.ahl-alquran.com/arabic/show_article.php?main_id=4239

Briefly:
• All the food is halal except what is mentioned in :( 5: 3)and other verses.
• After what is prohibited there, every meet is halal, regardless of who slaughters the animal, Christian or Muslim.
• Mentioning the name of Allah means all the meat which Allah made as Halal. The haram forbidden,(5: 3 )means it has not the name of Allah on it.
• We have to mention the name of Allah only when the trained dog or the beats and birds of prey catch animal, we can eat from it but after mentioning the name of Allah.
• According to the Quranic rules :
1-Haram here is exception, while Hahal is the general rule.
2- Not to make Halal Haram. Not to make what is lawful by Allah forbidden.
3- Whoever forbids the Halal is making himself a God beside Allah.
• : يمكن تلخيص هذه القواعد في الآتي: (1) الحلال هو القاعدة والحرام هو الاستثناء.(2)النهي عن تحريم الحلال(3)إعتبار تحريم الحلال شركا بالله تعالي واعتداء علي حقه في التشريع .
All details in this articles in our site. It needs to be translated for the all Muslims to stop this business of the so- called Halal meat. It is against Islam as they forbid what Allah makes lawful.
In this regard, I also say :
Reading the next verse ( 5: 5 )It clearly makes it Halal to eat from the food of the people of The scripture, Jews and Christians. In return, they have the right to eat from our food. The same in marriage; we can marry from their women and in return they have the same right to marry from our Muslim women.
It is surprise. But I am here in the U.S make this marriage between Muslim women and Christian and Jewish men according to the Allah’s law in the Quran.