A priest can still give a crumb.
Yes that is the way it is done. When the priest gets to the person, he breaks off a small chip and gives it to the person.
However, in the example the OP gave, the priests is giving a special communion to the person. I have seen it done, the priests after he is done with everyone, goes up to the tabernacle and brings back the special host just for that one person. It is quite a spectacle on Sundays.
In my opinion, it is an unnecessary spectacle for the parents or the person. I think it has to do more with pride than avoiding illness. If the person was so allergic to wheat that they can't even eat a small chip, then they would be sick all the time, because there are more accidental pieces of wheat in all the food that they eat every day.