Footballers' girlfriends on hotel beach are safe enough, because in Dubai you have to come to the authorities' attention for some reason in order for it to become a problem -- victim/perpetrator of a crime, pregnant and needing medical are (though not all clinics or hospitals ask for a marriage cert) like the woman in this case etc.
My now-DH and I lived in Dubai for a year and a half unmarried, for instance -- and while we lived there, the police were carrying out door to door checks in Sharjah, the next-door emirate, checking on the marital status of mixed-sex couples or groups sharing living quarters, and making arrests. We never had trouble, but were very much aware that if we were burgled or assaulted we couldn't report it, or if we were in a car crash (especially with an Emirati), we were in trouble.
People do get complacent, because Dubai is full of unmarried expats having extramarital sex, buying and drinking alcohol without a licence, living there longterm on a tourist visa etc - but most of the time it's under the official radar, if you're careful and lucky. DH was sponsored for a work visa, but as we weren't married, he couldn't in turn sponsor me, so I was on a tourist visa and used to do a 'border run' once a month with other unmarried foreign women without residency visas. Again, the authorities generally turned a blind eye to carloads of women who literally drove over the Omani border and turned around and re-entered the UAE.
Lots of prostitutes there on tourist visas used to do the same thing. (Once, when six of us, all female, were being driven on our border run by the Lebanese-Canadian, Arabic-speaking boyfriend of a friend, the border guards assumed we were prostitutes and that he was our pimp.) Technically, prostitution is illegal in Dubai. In practice, it's a huge 'black' industry -- every 'Ladies' Night' in hotel bars has a significant number blending in, looking for business. Like everything in Dubai, the grey area is huge. That's what tripped up this couple, presumably - they were unlucky with the clinic taking the official line.