Where does this belief come from? I've seen it repeated enough times. I wonder if it's knowable? Sounds to me like pure conjecture. Sounds to me we can only know in a couple of years when the history of these events is being written.
Last autumn I took a day volunteering at a refugee shelter in Stockholm. The people I talked to (all Syrian) couldn't shut up about how much they wanted peace in Syria so they could go home. I don't believe any of those are economic migrants.
I know we call the Afghans economic migrants because we've decided that Afghanistan is stable and peaceful. But it isn't. Civil war is still full on. That place was never pacified by the Coalition. Regardless what we chose to label them as in practice they are refugees.
As for the Africans that's been a steady stream now for years. There's no surge going on. We haven't suddenly got way more African refugees. I remember it was the same situation in the 90'ies. Nothing has changed. The fact that these keep coming doesn't mean that the Syrian refugees aren't refugees.
The number of those refugees makes it easier to hide among them, though. Greece was overwhelmed and couldn't process everyone due to sheer mass, as well as because due to EU rules the people didn't want to apply for asylum in Greece. What is going to happen is that internal border checks are coming back to Europe, sadly. "Papers please!"
It's super easy for a terrorist to hide as a tourist. I doubt it could be easier. At airports we only have "security theatre". Those checks only exist to put people at ease. But as for making us safe they're worthless. How many terrorists do you think they've caught in those screenings? The answer is zero, ever. I googled it... none ever. Any chemist can give you a list of ways to blow up an airplane that isn't screened for. Our greatest bulwark protecting us against terrorism is the incompetence of terrorists. In second place comes regular police work. Boys in blue, on the street, paying attention to weird behaviour and following their instincts.
We don't know why two of the Paris attackers chose to travel part of the way with refugees. It certainly wasn't to help them hide. There's just no need.