I, like you, am a FBSM type.   I believe fresh linens to mean that they have either a service or onsite wash/drier and they replace all the linens after every session.

No different than Hampton Inn putting a post it on your headstand that says "All Linens washed fresh for your arrival." or something like that.

Things like fresh linens, warm towels and proper massage tables are super important to me, so I like to know that the providers are thinking that way.

That there's fresh linens .  
It does not imply anything else.  
Do you honestly think any provider would give you a sheet or towel that some other bloke just used ? I know I wouldn't, It's why I allow you to use my washroom so you can clean your hands etc.
 Idk what you've been touching prior to coming in so, why would I want your unwashed hands anywhere near my lady parts ?
However, if you were going to a massage parlor ( a place with multiple rooms and employees I'll be the first to let you know that some places do sheet flipping & keep washcloths in a bleach water bucket .  
Sometimes it's best to not read into things too much or assume .
Like mister said it's part of the service. Xoxo V.

The linens are well broken in because I never change them, thats when you need to worry not when she says they are fresh.
 

Oh Jesus- sheet flipping? I need to go Purell my soul... In my case it means we have a linen service. I've noticed that studios that wash their own sheets have trouble getting their linens completely white- due to the fact that high-quality oil, such as grapeseed oil, is a FOOD and can discolor linens over time. No big deal, still clean, but some clients might freak if they see a slightly yellow stain on a sheet.