It’s usually possible to have privacy if you keep yourself private.
Since 2016 we have seen that although Meghan makes a big deal about wanting privacy, in reality her actions belie her words. From the very first reveal of their relationship, when Harry (at Meghan’s instigation, as he wrote in Spare) issued a press statement telling he world he was “'worried about Ms Markle's safety'” following the “wave of abuse and harassment” she had faced since rumours of their relationship first surfaced just over a week ago, her behaviour has been at odds with the often expressed compliant.
About the same time of course Meghan was snapped by friendly paparazzi photographers in Toronto posing happily with a large bouquet of flowers, and a necklace featuring the letters H and M. When the Palace press team warned her that this kind of choice would draw more press attention, not less, Meghan was annoyed that she was being told what to do. She’d also been dropping hints on her instagram - her and Harry wearing the same layered, brightly coloured bracelet, posts about her frequent trips to London to see a new love etc.
Then there was the same friendly paparazzi who took the first photo of Meghan and Harry out in public together in London, who publicly stated that he “magically knew where they would be”.
This is just more of the same.