Although it can be frustrating, once you get through the process, you don't have to worry about it, again.  As for sending that info, don't do it if you aren't comfortable.  Instead, start with known providers that have less stringent screening.  Then, you'll have a reference

Hope this helps,
TL

I was in the same boat about a month ago, except I am new to the hobby and had no references at all.  I was probably working with the same scheduler you are working with.  Ultimately, I opted to sign up on P411 because I though my information would be safer with them than the scheduler.  My P411 account has since sufficed for verification.  If signing up for P411 is an option, I would recommend that.  

I will say that now that I have worked with the scheduler, I trust her enough to send her a link to my linkedin page.  But that is a personal decision based on my own comfort level.  The advice I previously got was to not forward that information to anyone and go with P411 instead.  
 
I don't have a VIP account or else I would PM you the name of a well known and highly reviewed massage provider who did not ask me for verification.  
 

I am not sure why one would ask for LinkedIn profile or Facebook page alone since either can be faked.
However, combined with other info, both would be helpful in verification.

I've been a member for some years and found it quite useful.  I would not hand out a LinkedIn or Facebook id.  Keeping your real identity and your hobby identity separate is a wise idea.