Re: "In other words, not voting is effectively the same as voting to continue the status quo."
The majority (IE including those who did not vote) voted Remain.
Using that logic the majority in 1973 voted not to stay in the EEC (since only 67.23% of 64.62% voted "Yes") and the majority of the French voted not to create the EU in 1992 (51.04% of 69.69% voted "Pour").
People who didn't vote don't count. Trying to claim that people who didn't vote clearly supported your preferred option is just silly.