I had a fun go with this about a month ago. I signed up at the end of February as I had a lot of travel for work in March and wanted to see if there was anything I could do or Chase could do to expedite my upgrade to Plat.
I called the PC customer service line and explained my situation. The person on the phone said I needed to wait until the 60,000 sign-up bonus points were deposited into my account after spending the $1,000 within the first three months. I argued that wasn't the case and that wasn't a factor at all.
I ended up getting fed up listening to her babble on, so I called the Chase PC customer service number and the guy confirmed that merely being a card holder (as I thought) qualified me for the upgrade to Plat.
I called the PC customer service line again spoke to the 1st line of support and after hearing the same garbage, was transfered to a "manager" who at first spouted the same thing. I had asked "well, what if I never spend $1,000 on the card?" to which she had no answer.
I received the card the first week of March, spent my $1,000 the first day I had it in my hand and I'm still waiting for Platinum....patience...patience.. Ha!