"Sod over the area where the tree fell." What does that mean? You mean where the stump was or where the tree landed? I assume you mean where the stump was. What he likely did was grind the stump and leave the wood chips in the hole. That will be a problem. ALL the wood needs to be removed and replaced with topsoil or sand. You will have a problem for decades if you do not remove it.

Let me clarify - the sod is over the hole where the stump was removed and an area of the lawn that was damaged from the equipment they used. they did fill the hole with soil.

I'm stumped...heh heh.

It should not be squishy if they used real topsoil or sand. If they added any organic matter like sawdust, mulch or compost, then it will be squishy.