kawakasi push rods are really thin and bend real easy but that usually would not cause and engine to sieze
However one falling into the engine could and do a reasonable amount of damage to boot.
Right now, start journaling everything exactly as you can remember, dates, time and in particular operating hours.
What was said to you what you said to them.
Start emailing the dealer rather than phoning so you have a written record of what is said & done.
There are way to many shonks out there who just take the mower out of the box, fill it with oil then deliver in place of doing a proper predelivery.
They make it hard for the honest hard working ones who do things properly and push customers towards cheaper on line & big box stores.