It is basically as Michelle described.
Someone went to WDW and came back to the DIS. They were waiting for one of the parades, when they saw a family march up, take out a big piece of sidewalk chalk, and proceed to mark out a large spot on the pavement that they "reserved" for their family, and would tell people not to get into their "spot".
Anyway, that thread took off, much like this one has, and it went on, and on, and on . . .
Hey, that's the solution!
MIGrandma, you should just use chalk, or spray paint, around "your" picnic table, and maybe people (and kids) won't "invade" your personal space!!!