Seems wrong to me too.
There are predominantly 2 types of sulphate attack which affect concrete. Both occur naturally in most concretes but it is the level of the reaction which determines whether it is deleterious or not. Ettringite which is where reactive sulphates come into contact with moist portland cement and Thaumesite which is highly unlikley to have occurred in a house floor as it requires generally mobile ground water laden with sulphates. The former hydrates the cement to form a fribale weak crystal and is what often causes tile delamination with cement addy on gypsum screed and the latter basically turns the concrete to jelly and is a relatively recently diagnosed concrete pathology which affected a number of bridge structures down the M5 in the 1990's. Another issue which weakens the concrete is alkali silica reaction. This is where a reactive aggregate interacts with the hydroxyl ions within the cement pore solution. It forms an expansive gel which can seriously disrupt the integrity of the concrete. the concrete cancer scares in the 70's was predominantly about this.
Assuming there is a damp proof membrane under the concrete which would depend on how old it was it is highly unlikely that any of these are an issue in a house floor.
As for concrete giving off some sort of toxic dust - in my politest possible language - wot a load of bollards.
If there are visible signs of issues then fair enough but if there is nothing visible it sounnds like a bit of a con. I hope they have not parted with cash themselves to have this "analysis" done. The usual reason for core samples is to determine compressive strength, examine compaction and to carry out a petrographic analsis which looks at the particle distribution in the concrete. It is rare to see eother of the latter on an old concrete sample.
What age is the floor and are there visible signs of deterioration e.g. cracking, discolouration, pop outs or soft spots which can all be signs of various pathological conditions including heave, subsidence, shrinkage, substrate movement etc etc.
If the surface of the concrete is exposed why not just prime it and put some nice self levelling compound on it. Maybe even some nice quarry tiles....