As an alternative it could be argued that Murray has done more in terms of changing our expectations in his sport than anyone else. Arguably Bradley Wiggins in that first TdF win, or Mo Farah in his competition wins in long dustance running, did but most other successful sports people did so in sports where British expectations were already quite high. Even with Wiggins and Farah, if we take cycling and athletics as the equivalent to tennis, it can be argued that it was in the tradition of a successful British participation.
Murray's wins at a male Grand Slam tournament, Wimbledon men's, and the significant driver in winning the Davis Cup, all for the first time in over 70 years , and becoming the first British male to be ranked No 3, 2, 1 in the Open era is a step change from what was achieved previously.
But that is really a different way of saying that:
Murray has delivered more for his sport(which is tennis) than any other brit has for tennis in modern times
The point being that Murray's achievements are context specific - in other words in the context of a sport where Brits have done really poorly. But had Brits done fantastically at tennis over the decades, then his achievements would be fine, but nothing out of the ordinary. And I'm struggling with the notion of Murray somehow as the greatest British sportsperson of recent times when, arguably over the period of his tennis career he is probably only the 4th best (with Federer, Nadal and Djokovic ahead of him).
To my mind to be really great you need to be great regardless of context, so the best in the world over an extended period of time in your sport. So using that way of thinking then Wiggins has a claim, as does Hoy (in differing disciplines world beating in cycling over a number of years), also Redgrave and perhaps Farah.
So I don't think you can be the greatest just by changing our expectations, you are the greatest because you are the very best, regardless of expectations.