I am not aware of what particular postings on here have discussed a claimed 'biblical basis' for deceptive claims, but I take your statement and respond to it. This question links to people who deceitfully claim that they have been vaccinated when, in fact, they have not. This with regard to Covid-19 vaccinations.
In Britain, government seems set to insist on proof of vaccination, or of currently being Covid-negative, before allowing people entry into certain large, public gatherings. This seems to be initially aimed at an age group from teens to 30-somethings who frequent popular music events, either outdoors or indoors, and at a broader age group who go to large sporting events. It is guaranteed that some of those people will fake proof of vaccination in order to get to those events. But it is questionable whether any of those ones would even claim to be Christians. If some do, then they are hypocrites and liars, and the Bible is crystal clear that such ones are not in the Kingdom of God to begin with, nor will they get into it (without genuine conversion and repentance.) They fool themselves, and some others, with claims to bear the name of Christ. Nobody fools God.
But you ask if it's legitimate for a website invoking Christ's name to allow discussion of whether deceptive claims could have a biblical basis. Sadly, there are some people who invoke Christ's name (or the name of some other whom they worship) who believe that their holy books allow for deception in order to either promote their religion, or to get themselves out of a difficult situation. The question is, does faking vaccination certificates involve such matters?
Christians are free to exercise their consciences when it comes to vaccinations (the Bible does not say a word about such modern medical procedures). Some do feel it is ethically un-Christian to accept any vaccination that has been initially based on use of farmed cells from aborted foetuses. That has rightly been asked about on here. Yet is there a chasm between that and the ethics of lying and deceiving others into claimed receipt of vaccination? Perhaps there's a wobbly bridge between the two, but I think that anyone trying to invoke the Bible in support will find themselves falling off their wobbly bridge into a chasm of spiritual disaster.
As a trinitarian Christian I am repelled by anyone claiming to be a Christian who thinks there can be legitimate use of lying and deception. I have had to repent of that myself, in former years, and am becoming more aware of the evil nature of anything short of truth and honesty. There can be situations where silence, or not answering a compromising question as expected is the course of wisdom - Jesus often fielded wrong / bad questions by asking his own right / true questions instead. And, at the end, he kept silence, even though that contributed to his unjust death.
All of that is so far removed from today's vaccination deceivers that I have to conclude that such people are so self-centred, so selfish, so carnally minded as to the pleasures of their short lives that they cannot claim to be Christians. Yet this site may inadvertently cause them to expose themselves by allowing questions such as you ask about. When we come across questions that are offensive to us, we have the choice of down-voting, or of responding to show why the question is offensive. Thirdly, we may treat the question with the contempt we feel it deserves by utterly ignoring it. But as this is not a Christian site - it asks about Christian issues - we must expect offensive questions, and answers, if we have spiritually Christian-sensitive consciences. Most people in this world do not.
My answer is that it is within the current policies of Stack Exchange, and it is certainly being practiced, but perhaps now would be a good time to think again and perhaps tighten up certain policies and practices.