PCA shows overlapping boundaries, then why SVM performs best
I assume you applied SVM to your initial data and use PCA only for visualization. I this case:

I guess your projection via the PCA is not showing the real picture.

You should check first how much of your data is explained with the first two principal components of the PCA. Your projection might change to much the structure of your data so that its not seperable anymore. In case the projection to the selected principal components is not changing your data too much, it could be that you maintain the seperability.

Finally, note:
If the projection is linearly seperable, then so is your data.
If the projection is not linearly seperable, you cannot conclude about seperability of your data.