Most people associate "wants to spend time with me" as "cares for and values my company".
Let's cancel, I'm too lazy to get out of bed
I don't care enough about you to get out of bed
I know we had plans, but I can't be bothered
Most people would cover it with a white lie so it sounds better, which is probably why she mentioned that. Is it bad to be honest? No - now she knows where she stands.
I am not surprised she is shocked, especially as you are in such a new relationship. Typically couples are still in the "honeymoon" stage of being excited to spend lots of time together, and still learning about each other's relationship styles. Now she may be wondering, "if he isn't motivated to hang out with me when we had plans, does he even care about me? if he doesn't care that much about seeing me, what future does this relationship have? if he's already so settled that he won't get out of bed, why should I be putting in effort?" Or she might be thinking something else!
The bottom line is, you need to find out why she is so upset and resolve it. Relationships are not about who is right or wrong. You cannot go to her and say "ha! the internet said you shouldn't feel this way!". For a relationship to work, you need to understand her point of view and find some solution that you are both okay with.
Personal experience: I've been on the receiving end of such behavior from a boyfriend. He said he would come to lunch with my family, but the day of told me he was too lazy. I was very upset. He might as well have said "Yeah, I know this is important to you, but I don't actually care" - in fact, that's almost verbatim what he said when I asked him about it afterwards. Yes, he was honest, but that didn't fix the problem. (We broke up a month afterwards - this was an indicator of why.)
Now, family plans are perhaps more significant than hanging out, but the same principle applies. When you're earlier in a relationship, you aren't as secure, so something that might be less of a problem later in a stable, long-term relationship will still cause big problems now.