"No good deed goes unpunished." -- Clare Boothe Luce
If you're asking for a fixed-price or a time estimate, they may want to see the back-end of the site in order to evaluate how much work is needed. If you know how, perhaps you could make a copy of the site for them to look at (and also remove any confidential information from it).
I can not say what is right for YOUR situation, but I can tell you:
As a client, I would not let complete strangers have access to critical systems. A complete stranger would work on a copy or development version.
A trusted freelancer may well be granted complete access to all systems.
As a freelancer, I am often granted complete back-end access to servers and databases. This often happens before I am officially hired. Maybe clients are more likely to trust me because I have an established work history.
A single answer may not apply to every situation.