Do you have a copy of the actual page from the PAisley poor Law records? Or is this just the information you got from the on-line index?
If you haven't got the original document, I think it would be well worth sending for - the few I've seen contain much more information than the index.
It sounds from what you say, that she applied for relief from Paisley, but they will not have wanted to spend money if there was someway out of it, and if she was 'sent to Perth', then I'd suggest that is where she came from, and they would have sent her back there. It's unlikely she was tried in a Paisley court as you suggest. The Poor Law board had the power, as far as I understand it, to make these decisions.
Do you know for sure she went back to Perth?
If the decision of the Poor Board was not to pay her, and send her to Perth, I don't think they had any power to actually force her to go - they just wouldn't give her any money.
I have an ancestor who applied for Poor Relief, but the decision of the board was to not pay her and to send her back to where she had resided previously to Paisley (although she had lived in Paisley before that). But I know she didn't go. She is in the next census for Paisley, and then died there. She must have found some other way to survive without any help from the Poor Board.