In this I would lean in the direction of the government simply because parliament has waived the decision by way of holding a referendum, which may or may not be legally advisory but politically is not. If MPs wanted to reserve the decision on leaving the EU for parliament then they should never have voted to have a referendum. I don't think at this point parliament has any right to intervene, nor is their contribution especially useful since they cannot bind the government in negotiations. I am not seeing a point to this unless they intend to block it, which they won't if they value their jobs.
Consequently I am disengaged from all this and if I understand the vote last night, that is largely symbolic. The only real justification that now stands is that parliament must have at least have some clue what the government is aiming for to ensure the PM is at the very least sane.
But even then that is stretching it. Parliament wants to be involved to avert a hard Brexit but invoking Article 50 and electing for a negotiated settlement is by definition not hard Brexit, and if they were at all issue literate they would know that Mrs May is seeking to avert a cliff edge. She has even said so. How the government shapes that is entirely the government's business as the executive.
What I would note though is that this wouldn't even have been an issue if the leave campaign had set out a particular set of objectives and a roadmap for getting it. Had they set out a credible alternative to EU membership and one that could be considered sane, parliament would know what the direction of travel was and would have no real mandate to intervene. The uncertainty and incoherence invited exactly these shenanigans.
Meanwhile Twitter is awash with damp toryboys praising various politicians for their "superb oration" in last nights debate. Thing is, if I want to listen to eloquent people spouting off entirely generic rhetoric there are any number of places you can hear exactly that. It is not the mark of a good MP. Even the loathsome Mhairi Black can on occasion rattle off some sincere and impressive rhetoric. What marks a good MP is someone who has bothered to familiarise themselves with the issues to a degree one might expect from people whose actual job it is to know the details.
MPs are paid to know what they are saying - they have a generous allowance for staff to do their research, they have the HoC library, the resources of government which they can tap into via parliamentary questions, and they have select committees which can be used to explore issues. As individuals, they have absolutely no excuses for being ill-informed yet still we find them wide of the mark. We might then ask what the point is of giving them the opportunity to scrutinise when they are manifestly incapable of doing so and wouldn't bother even if they weren't?