hopeonly,I believe a US citizen filing for parents may have its advantage because of the immediate relationship factor. That may allow them to stay here and procure the green card here in the country itself and the present expiring status may not be a topic of obstacle, but it is definitely not the same for students or employees adjusting the status, they have to have certain status while adjusting be it TPS or any other non-immigrant instances. The 'out of status' factor can be detrimental in their cases. I hope if somebody knows better or more, please pitch in, because I am not a lawyer as such.
The only thing that may or may not be an issue would be if your parents are asked why did they use the visitor visa to adjust the statuses as the intent of this visa is non-immigrant. They came to the country as 'tourists' but now they are immigrating. This I am not sure if will be a red flag. It varies cases to cases that is for sure.
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