So... is it normal to be able to rattle the back wheel like this?

Yep, if you're not surre and it can go bang, seize, or fall off and
probably hurt or kill you in the process, then pay someone else to fix it.
Bit more piece of mind. (and if it still does and you walk away, you've
got a warranty!)
IMO you got a good result for a good price. Cheers

 

Two good reasons why people like that deserve plugs like that.
There should be more of them (both!)

 

He may well have done (!) but when I saw him (if it was him) he was
walking out of an office in the shop.

Although, when I saw the guy I had no idea who he was. A few days
later I saw this picture and thought "Strewth! The likeness is
remarkable. Could it be?"
http://www.taylormotorcycles.com.au/assets/images/staff/geoff_taylor_lge.jpg

 

He may well have done (!) but when I saw him (if it was him) he was
walking out of an office in the shop.

Although, when I saw the guy I had no idea who he was. A few days
later I saw this picture and thought "Strewth! The likeness is
remarkable. Could it be?"
http://www.taylormotorcycles.com.au/assets/images/staff/geoff_taylor_lge.jpg



Nah, doesn't look the bloke I raced against, he was much younger
Although that was in the late 1960's, so he may have changed a little