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aggi
I mean that they should be able to work out if an intrusive survey is required. A stud finder should be able to tell them the direction that the joists run in without any invasive work being carried out. They can determine the approximate thickness of the joists by looking around the staircase for a measurement. The biggest indicator however would be by being above the area where the wall was removed if the floor feels like it bounces when walked on then there are issues.
Without getting too boring there are easy formulas (and tables for the hard of thinking) that determine the maximum span of a joist. By knowing the direction that the joists run in and their approximate thickness (they come in standard sizes so the actual amount of guess work is very little). They can determine fairly easily if support is required from below. Also if the wall was running in the same direction as the joists it is MUCH less likely to be load bearing although not impossible.
NB all of this is assuming there is not a wall on the first floor above where the now removed wall was