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This exact same thing just happened to me. I don't have enough money for FSW and I told them that, but they sent me an ITA anyway. You have to prove you have it in the bank for 3 months also, so keep that in mind. If you apply for FSW (telling the truth about funds at your disposal) and get turned down because of insufficient funds you will lose your $550 application fee and be back where you began, right?

So frustrating! I have 507 points. I was also one of the CEC applicants that got duped by the false quota information on the CIC website last fall. I think I'll have to decline the ITA. Apparently if you don't have funds but if you do have "arranged employment" ie. a job with an approved LMIA or a provincial nomination you are still eligible for FSW class. I can't get those though, they're very time consuming and expensive to obtain.
 
Please remember that as long as you qualify for both FSW and CEC, the system will always generate ITA for FSW
 
Oh, thanks for this! So helpful.

I declined my invitation :-X

I changed my funds to $1000. I think I can safely say I have that much at all times.
I said that I don't have a "job offer"... what a misleading phrase. I'm currently employed and have been living in Canada for 5 years.
My EE profile says I still qualify for FSW, will that be updated?
 
Yes it will get updated......just make sure you say No to job offer question and also ensure that you submit the profile after making changes, i.e., where you enter your name and secure answer and click submit or transmit. The profile should be updated after some time.