I think that they are correct in theory - we have a parliamentary system and Parliament should be making decisions wherever possible.
The issue here is in the practice. We all know that Parliament will not decide/agree on any particular form of Brexit. Labour, as they currently stand, are no more than an anti-Tory protest party - same goes for the SNP. The Lib Dems won't go for any kind of brexit at all, and the Conservatives are split down the middle.
So if we can't reach any decision (and I think it's a very safe assumption that we won't), the result will be to keep the status quo. Whilst some are able to argue (incorrectly IMO) that no particular type of Brexit was voted for and therefore cannot be defined, the one thing we absolutely know the majority voted against was the status quo.
So the only solution I can see is that we give parliament a limited time to come to a decision after which it is in the hands of the PM because the least democratic result of all is to keep the status quo.