Kluger,
this is complex and unclear stuff, so let’s try to be accurate:
1) as I mentioned above, “vaccinated covid PATIENTS have exactly the same viral load” does not mean that vaccinated PEOPLE are the same risk to others: because vaccinated PEOPLE have less chance of becoming PATIENTS. All of this when you compare same demographics and same behaviors.
2) you may be misunderstanding something or you are using secondary sources that misunderstood or misinformed you, or maybe someone used inaccurate language. Could you give me a reference that I can check out this data. “CDC says” – maybe author and date or newspaper article title.