In saying "The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all.", I believe that Singh is implying that in using a cipher, Mary and her recipient felt much safer than if they had used no encryption at all. They believe their message is secure, so they do not feel the need to be discrete in their language. Had they not used any encryption, the content of their messages would not have been nearly as direct as it was with the encryption.
For those who attempt to keep their communication secret through encryption, this statement implies that their encryption method needs to be rather strong if they expect it to be effective at concealing their messages. One cannot hope to use a simple Caesar cipher effectively, as that encryption method is rather weak. It could be cracked by even the lowliest of amateur cryptographers in a small amount of time. The fact that Singh describes the cipher of Mary Queen of Scots, an encryption method that I couldn't hope to begin to comprehend, to be weak implies that for an encryption method to be effective, it must be very complex. This tells me that unless you and your recipient are seasoned cryptographers, you shouldn't bother trying to encrypt your messages, for one could decrypt them with ease. Instead, you should try to use more discrete language and keep in mind that your words could very well fall into the hands of your enemies.