They pack everything unless you don't want them to pack something.
We packed clothes and higher valuables (jewellery & watches) into suitcases ourselves and they did the rest.
It's something they do every single day so i guess the key is just having the mindset that they couldn't care less about what the items are or who you are. It's only you who'll feel awkward...
For me, the convenience and stress relief of them doing that work is so much more than any feeling of intrusion.