mandz
Looks perfectly ligit to me.
I'm going to a privately rented apartment too, in Los Cristianos in just under two weeks (owned by one of the other HT members) I have never met the guy who owns it or his wife,and I can't see why you'd have any problems to be honest.
P.S. I presume you've got plenty of contact details for the owners,since you've paid your deposit etc...
I'm sure everything will be fine,and you'll get keys etc. to the apartment in plenty time, before your holiday.
Have a good one,I envy you going at that time of year.