The way I see it, is that these are two separate business arrangements. One between you and your gardener and one between your neighbor and her gardner. The fact that it's the same gardner is irrelevent. If you both shop at the same store and she doesn't pay her bill, the store doesn't ask you to make up for it...and it's just as innappropriate here.
Personally, I wouldn't bother saying anything to her. The garnder shouldn't have said anything to you and it's none of your business.
So, him asking you for an advance (which is a red flag for me), is a stand alone request. If he wants to pass on excuses to you of why he needs them, that's fine, but you don't owe him anything.
If anything, I would talk to him. "Gardener, this is the third(?) time you've asked me for an advance. We agreed that I will pay you for the service you provide, after you provide the service. Yes, I've made exceptions in the past, but this can't continue. If you want to remain employed by me, then you cannot keep asking me to bail you out when another client doesn't pay you, or you have unexpected bills, etc. You run a business and your clients aren't responsible for your financial shortfalls. Please don't ask me again."
Also, I'm with you on giving people the benefit of the doubt and would likely not have a problem giving a good employee an advance the first time they ask...assuming that it is truly an emergency situation for them. That being said, I wouldn't continue to give someone the benefit of the doubt if they continuously turn to me to solve their financial problems. There's the inital assumption that someone has good intentions and then there's a point where enough is enough.