A lot of recurve bows have a lot more shaping/protrusions of the riser/grip area on the belly side of the bow which could throw the measurement off, at least more so than measuring along the back of the bow. ( The pix illustrates that a little, but in fact, the line would follow the contours of the riser). That's why it's important to measure along the back of the bow, as Charlie suggests.
There's obviously a lot of confusion on this though, in part, because folks also often confound back with the belly of the bow.
Sort of like measuring draw length. There are enough of us who do it differently that it's wise to determine how the other person is doing it if we want to be comparing apples to apples.
And knowing the bow length still only gets one in the ballpark re string length. The AMO standard is a string 3 inches less than the bow length, regardless whether it's a recurve or longbow. Of course, the old rule of thumb is 3 inches shorter for a longbow, 4 inches shorter for a recurve. But, depending on bow design, and how the bowyer measures bow length, neither of those may be spot on either, but they should get you in the ball park.