I am not exactly sure how it works on nexus because ive never owned one, but you should be able to 'sideload' the OTA with the stock recovery. There should be some kind of button combination that gets the phone into recovery that you hold while booting
I dont think you need a pc / android SDK installed, but I'm not positive,
on my phone (gs4ge) you do need the SDK because the OTA file must be sent through it, in older android versions I could have it installed from the sd card, but they took it away for some reason with kit kat. My recovery wont install OTA's located on internal storage so sending from pc through sdk-tools is the only option. Lame, I worry it may be that way on nexus too.
this is possible with total stock, unrooted etc, it is a legitimate process
I cannot wait for 5.1 then on my Necus 6 as I am disheartened by refreshes when my Moto X 2014 is fine.
Can one get an apk file to update to 5.1? I do not root or do android sdk, I would not even know where to begin.