From water pump thermostat and radiator to bad heads

Car started leaking coolant which we noticed after it got hot one day, but we never let it overheat. We put some coolant seal in it and seemed fine for a few more days until we saw a more severe leak, again it got hot but never even hit hot. We then had it towed to a mechanic who said we needed a new water pump and thermostat after he replaced that he says the Bars gold coolant seal we put in it when it originally overheated caused a clog in the radiator so we had that replaced as well. Now says the car blows coolant out the exhaust with a cloud of white snokCar started leaking coolant. It got hot but we never let it overheat. Brought it to a mechanic who said we needed a new water pump and thermostat after he replaced that he says the coolant seal we put in it originally caused a clog in the radiator so we then had that replaced as well. When we are suppose to get it back he tells us the heads are bad as there's coolant coming out the exhaust with a huge cloud of white smoke. We never saw white smoke ever and before having it towed to his shop we did have to move it a few times from parking stall to parking stall two seconds from each other to avoid being towed by the city So my questions are:

How did he not know from the gate the heads were bad?

Does this sound like a legit story from our mechanic? Or possibly a mechanic error he's trying to cover up?

If it sounds like a mechanic who's covering something up he did, what would or could it be?

Thank you, Gavin and Tiffany