I am also working in a company with very restrictiv IT security settings, well, it is the IT department of a bank 
Interestingly, I am able to install Obsidian to the local drive of my laptop and I can use it by creating a local vault - which I did. So I use Obsidian in the company with a own vault where I only have company related notes. The IT security is very keen on blocking access to any kind of cloud drives, ftps, sftps, ⌠understandable, as we are wirking with customers data. So a web version of Obsidian would not help me, as the access would be blocked by default.
I could not even request access to the webversion, as it is not a company certified solution and the security guys would say that I have everything what I need for work pre-installed on my laptop - and this is true.
So I am happy that I can install and run Obsidian on my companys laptop, even if I do not have access to my private vault.
Cheers,
Peter