To quote the relevant Wikipedia article:
The original creators of the database keep a list of some of the methods tested on it.[7] In their original paper, they use a support-vector machine to get an error rate of 0.8%
Feel free to look up that original paper, but to me the quote strongly suggests that the first record holder was a support vector machine.
Edit
As liori points out the quote is misleading: In the original paper Yann LeCun et al. actually tried a slew of methods and one version of ConvNet scored best (0.7).
But according to the MNIST-webpage, after that initial paper, DeCoste and Scholkopf, MLJ 2002, reached an error of 0.56 with a SVM. So if that webpage is complete, the claim is still false.