Spoke about this in more depth to DP; a while ago now but was a qualified technician for a major brand.
They had the capability to crack into a laptop / desktop computer without a password, but absolutely would not do it without original proof of purchase (or on occasion the original owner's death certificate). Even they couldn't crack a phone or tablet without the password, they could only wipe them clean - albeit still linked to the original owner's account.
Different brands will be different, but he'd expect one or the other to be required by any legit technician. Anyone who doesn't ask for some personal info to get into your machine is probably cracking and wiping stolen goods under the counter on the regular.
Run of the mill for them to stream something to check internals are all working. Often YouTube but if a client had a streaming site bookmarked and logged in then not out of the question they'd use that, quicker and easier.
Shockingly to some on this thread a technician who's fixed your device does have access to all your data and will definitely skim through it (including photos) when copying from one device or drive to another to check for errors or broken files, but they do it all day every day and couldn't give a toss about trawling the finer details of the content, even if they had the time.
What they didn't do was drop everything and binge a 12 hour series (These are out and proud geeks; if they were that desperate to watch anything specific they'd find and download it elsewhere).
This is just his experience working for a big player circa 10 years ago, different brands and companies will have different codes of practice.