Every now and again Twitter tweaks its block function. The most recent one that I was aware of was to separate blocking from reporting - they made it easy to 'no blame' block someone (if they look like a pretty irrelevant account that sells widgets and you happen to have mentioned widgets once) or to select from a range of options if you wanted to report a more troubling account.
In their 2 December 2014 post on improvements to harrassment, blocking and things like that they said
"Additionally, accounts that you’ve blocked won’t be able to view your profile."
I've asked the post's author about this... because I think it might lull people into a false sense of security.
@shreyas "Additionally, accounts that you’ve blocked won’t be able to view your profile" - ppl can just log out or use another account yes?
— Jo Brodie (@JoBrodie) December 4, 2014
To be honest this was how things used to be a couple of years ago and then, because* everyone would either just log out or view with a different profile Twitter let everyone see everything, so at least people would know that a block doesn't make any difference to someone's ability to see tweets.
(*possibly not because, it might not have had a causal relationship to be fair)
I'm not sure why this has changed again. My worry is that quite a lot of people will think that if someone they've blocked can't see their profile / tweets then they're 'safe' from that person seeing their tweets. I don't think this is true at all.
It would seem that there is no way to protect a user from an irritant seeing their tweets other than for them to make their account private (even that can be imperfect, see posts below).
An improvement might be to make it impossible to see any tweets without being logged in (but that doesn't solve the 'using a different account' scenario, and it doesn't seem to be what Twitter wants as it presumably it wants to share its content to draw in new users).
I'm basing my assumption about what people understand about Twitter and the block function from the search queries that bring them to my blog. A couple of years ago I wrote a post and have kept it up to date, it turned out to be quite popular and as far as I'm aware is still on the front page of searches for things to do with Twitter blocking (126,000+ people have viewed it) and as such I get to see an awful lot (13,000 searches) of people wondering what happens if they block someone. Most don't seem to understand what happens, which worries me.
In most circumstances you cannot view private tweets, but it's still quite leaky.