Do proceed with caution. The realtor is primarily concerned with one thing...getting his/her 3%. Remember who the realtor is working for. Hint...unless you have a buyer broker, the realtor is not woorking for you.
While this home may be attractive, don't rush in until you have full knowledge of the defect. It's better to cancel the contract and then renew negotiations at a later date (more leverage for you) than to jump in and have your dream home turn into a nightmare.
Clay soil is expansive. It moves as it goes through wetting and drying cycles. Houses can be built to be stronger than the movement, they can be built to keep the water away from the foundation or they can be built to do both.
I don't recall if you mentioned the age of the house, but sometimes slabs can crack simply due to settling occuring during the first few years after construction. Growing (or groaning) pains, so to speak. Or the slab could have a curiing/shrinkage crack from to quick of a cure during the initial pour.
You (or your realtor) could also ask the current owners who did the repair to the slab. If it was recent...within a few years...they may still have a job file on the project. They may also be able to add info to the riddle of why the slab cracked and the likelyhood that it will crack again.
Could have been a heaving crack (bad) due to expansive soil or a simple curing crack (not as bad).
A good inspecctor who is familiar with your area should be able to diagnose WHY the slab cracked, and give an idea as to the effectiveness of the repair. It may also result in the need for a soil test/analysis and a bit of engineering. Still, a good inspector will be able to hold your hand through the process.
I'm not sure what type of building officials you have out there, but try talking to the building inspector and see if they can give you any advice on what methods of construction are preferred.
Leave the final recommendation to the experts. It's tough to try to detach yourself from a house you've already fallen for.