Firstly, Logic can and does use the internet.. There is a check at startup for example... that bogged down some Users Logic startup sequence. On top of that on some OS X configurations.. it also constantly tries and retires to connect to Airplay so that's another possiblity.... especially if you use something like Little Snitch which can, by default, block it without you realizing.. causing the issue to be made worse.
One of the other parts of OS X that can bog down Logic is the good old mdworker (and/or mds too) routine, used in Spotlight for example.. that Logic heavily relies on to find everything it needs... and as does Kontakt too.., that can bring Logic to its knees for quite a while, when it (mdworker/mds) gets stuck in some form of loop... and becomes a 'runaway routine' using large amounts of CPU and other resources for no good reason... only to suddenly fix itself for no good reason either... releasing Logic (and other parts of the OS) back to normal performance levels.. This one plagued me for a long time with Lion... but then, out of the blue one day it just stopped and it wasn't due to anything I did or didn't do.. and nor was it corrected by any updates because there hadn't been any for at least 2 weeks prior to it correcting itself. I never did work out it's cause or it's cure.. but it is something that if you search Google for "mdworker issues' you will see lots of people reporting similar issues (in both Logic and other apps) to what you described in Logic and that I witnessed myself too.
I thought it had been finally fixed in Mountain Lion but no.. as one of my clients had a nasty attack of the mds's only a few days ago and we had to step him through destroying/rebuilding his Spotlight indexes again to fix the problem and for once that fix actually worked (which often it doesn't when it's mds/mdworker related...and not anything else spotlight related)
Another thought is.... Piano in Blue is quite a demanding library for Kontakt so I would try replacing that with the standard Logic Steinway if it happens again and see if that releases things... (That would eliminate both Kontakt and PIB itself, from the equation)
What version of Kontakt are you running? Is it the newer 5.1.0? I ask because I have some issues with 5.1.0 that NI are currently working on with me.. (Sudden and dramatic increases in single core CPU usage and what appears to be a severe memory leak..that is intermittant) . I didn't have any issues with the previous 5.0.3 release.
Personally I think, from your description you had either an mdworker issue... or a network related issue.. but given how complicated everything is.. and how many different interacting parts there are to all of this, it's just a guess... but the fact it suddenly fixed itself, makes me think mdworker/mds simply because the exact same kind of thing happened to me too.