Non-dom status has been around FOREVER. It allowed people to only pay tax to HMRC on UK income whilst claiming that they were only temporarily in the UK.
The statement thrown out by Murty's PR spokesperson saying that India didn't allow people to have multiple citizenships is a red herring. Tax domicile is not citizenship, the two are not related. Many people with other citizenships who come here from other countries automatically become domiciled in the UK for tax purposes because they usually don't know about the non-dom thing and quite frankly don't care. They usually don't end up with massive stockholdings worth over 7 figures with annual income streams from dividends in the 6 figure range. And they cease to be domiciled here when they return to their home country after several years, tell the HMRC that they no longer live in the UK, don't intend to live in the UK and thus are no longer liable for taxes due to HMRC after a set date (usually when they leave the country), and there's no problem with that.
If you read the legislation, if you're resident in the UK for more than 187 days a year (that's just over half), you are considered tax resident (and domiciled) here, unless you actively go and tell HMRC that you are not, and that you don't intend to be (and you show proof that you have a home elsewhere, family ties and the like, which you will return to eventually). That's what Murty's done. She says she is an Indian citizen (not disputed), and intends to return to India to take care of her parents, etc etc etc (so far not disputed by HMRC either).
So, Murty could have simply started to be tax domiciled here in the UK without a fuss. She would've had to pay tax on her worldwide income here, subject to double-taxation agreements (DTAs). India and the UK have one, as do the US and the UK, so the UK's view would've been 'tell us how much you paid on your income elsewhere, and we'll either "credit" it to what you are due to pay us or we'll ask you to pay tax on what you've not been taxed elsewhere'. If India doesn't tax investment income like interest and dividends at all, then she would've had to pay tax on that here. If India taxed her investment income at a higher rate than here, she wouldn't have had to pay anything at all, and if they tax it less than the UK does, then she would've probably had to pay the difference here. The IRS in the US works on similar constructs. Everyone would've had their cut, and no-one, not even the most shrill of politicians in the UK, would've had a problem.
The problem is that she paid her taxes on her worldwide income in India (no problem there), and then paid the HMRC £60K to not ask her questions on any other income other than the UK income she gets. It's not ideal. She didn't do anything wrong (technically), but when her husband starts upping taxes and cutting benefits on those who have lived here all their lives and who don't have a nest egg they inherited from their father that leaves them with £11 million a year in dividends alone like his wife does, then yeah, you can be guaranteed that the optics are positively crap and make him look like the "do as I say, don't do as I do" kind of person that (unfortunately) he turns out to be.