This is false. The virus in the vaccination is vaccina, after which the process was named. Our parents had us get vaccinated. How many problems were there then?
Yes, the current version of the smallpox vacine is vaccina. The previous version was real smallpox in a weakened form cultured from infected cows. The problem with the old variety was that it was difficult to maintain quality standards, so it was often totally ineffective.
The new stuff sets a much higher standard for quality, but it has more side effects.