Pianotech

I have received a request to tune for a local concert series that will be held in a church. 

The event coordinator would like me to bill them directly, in advance for the 6 upcoming concerts to make it easier for them to "process the payment". 

This makes me uneasy. Normally I bill the venue, not the performer, and I would like to do this here.
Part of the reason for this is that the piano belongs to the venue, and it seems like it is therefore their responsibility to maintain the instrument. 
Also, the venue will have to schedule the tuning work with me as well as make sure someone is available to let me into the building. 
Furthermore, what of additional repairs? (I don't anticipate problems, but what if a bass string or agraff breaks, or something more catastrophic happens?)

What would you do? Part of me feels like just sending him a bill, and letting them do it the way they want. 
I am worried that I am setting myself up for potential (if unlikely) liability issues by billing the wrong party for the work. 

I'm likely way over-thinking this, but I would love to hear what other people think on this one.

Thanks Wim, I appreciate your helpful feedback. 

Hi Jeremy:

I would bill the person or entity that is hiring you.  I don't know the arrangement that the promoter has with the church, if it's a fundraiser  for the church, or the church is just renting out their facility.  But your obligation is always to the one who pays you.  As far as repairs and anything that might happen to the piano, that would fall to the owner, in this case the church.  If the piano is being rented along with the venue, the risk is on the one renting it, unless of course it's been abused during the performance.  You won't have any problems or liability for not billing the right person or entity.  But it doesn't hurt to ask if you're uncomfortable, and if you have a regular gig tuning the piano, you know who to call.

Thanks Paul, this is helpful.