These claims will be widely made in the heat of the UK's referendum campaign. They make no sense.
First, when these statements were made, the identities of the bombers were unknown. There were unconfirmed reports that Arabic as well as French words were shouted just before the attack in Zaventem airport, but that hardly demonstrates the perpetrators had just arrived from another country. What is known is that Brussels has one of the highest concentrations of extremist cells in Europe. They don't need a Schengen visa to drive up the road to the airport.
Second, let's accept that the bombers did have to cross a Schengen border to carry out their attack. That's certainly possible, but would border posts prevent them? Belgium is not separated from its neighbours by 40km of water, as is the UK. So the border controls that existed before Schengen, and which in some cases now do again in the wake of the refugee crisis and last year's Paris attacks, conduct only partial and random checks on the immense flow of traffic crossing Europe's internal frontiers.
When they do, there is no guarantee border police will understand who is in front of them even if they stop the right cars. Salah Abdeslam, wanted after the Paris attacks, was stopped at a police checkpoint on the road from Paris to Brussels. He was let go.
Finally, what does this have to do with Brexit anyhow? The UK is not part of Schengen. It already controls its own borders. And there is no threat of the UK being forced to join Schengen - it can't be forced. Inside or outside the EU, London still won't be immune from terrorist attack. The July 7, 2005 bombings on the city's underground system were carried out by young Britons who had travelled, not to a Schengen country, but Pakistan for training.
2 Fallacy: This vindicates Assad.
Social media was quickly filled with comments that because the terrorist attacks in Brussels were (presumably) conducted by jihadists, this proved that distinctions made in the West between rebel or opposition fighters combating the regime of President Bashar al-Assad, and terrorists fighting him from Isis (Islamic State) are nonsense. Assad himself made a similar defence in a recent interview with Paris Match.
Syria may have become a magnet and manufacturing centre for jihadist terrorism, but that is thanks to Assad's actions. He described unarmed protesters as terrorists back in 2011, in order to justify the brutal methods of his security forces as they shot into crowds, arrested opponents, tortured them and made them simply disappear. At that time, there were no jihadists fighting in Syria. Isis didn't emerge until 2014. Those who took up arms against a murderous regime were not, and mostly still are not, terrorists. If Isis turns out to have organised the Brussels attack from Syria, it will change nothing.
3 Fallacy: This vindicates Russia.
The Guardian's Shaun Walker tracked a range of inappropriate responses from Russian and Ukrainian officials. The chairman of the Russian Parliament's foreign policy committee, Alexei Pushkov, for example, tweeted that: "While [Nato Secretary-General Jens] Stoltenberg is busy fighting the imaginary 'Russian threat' and putting troops in Latvia, under his nose in Brussels people are blown up."
Just a thought experiment: If Moscow had been attacked by terrorists in the last six months, would that have been the fault of Russian President Vladimir Putin for sending jets and bombers to buzz Nato airspace; or conducting large scale military exercises designed to intimidate the Baltic States; or even intervening militarily in Syria?
Ukraine's intelligence chief, meanwhile, promptly announced his equally unfounded suspicion that the attacks were part of Russia's hybrid war against his country and the West.
4 Fallacy: This serves Europe right.
Turkey's pro-government newspaper, Yeni Safak came close to celebrating the Brussels attacks, noting that it allowed Kurds to protest in Brussels when Prime Minister Ahmet Davutoglu was in town to negotiate a deal on refugees. In a tweet on the attacks, it said Brussels was "in the lap" of the PKK (Kurdistan Workers' Party).
This fits with the Turkish Government's efforts to equate the PKK and Kurdish fighters in Syria with Isis in the eyes of the world. That's an argument to have, but it won't be won by suggesting Europe's tolerance of Kurdish protests against Turkish policies invite attack by Isis. Like other such attempts to use the tragedy in Brussels for other ends, it is just tasteless.