Memory in dreams: fake or truth?

At the first, I must admit that I'm specialised in neither dream nor memory. What I'm desribe below is just my experiences.

Question: can we access our whole memory while dreaming?

I have a dream recently which I won't cover details here. What interested me is a pouch I own in reality. When I was dreaming, I strongly believed that it is used as a wallet, and I actually used it like a wallet in my dream.

However, in reality, though it do contains some unused coins, it is primarily used to keep important documents such as passport and other ID cards. You can imagine the size of such a pouch. Obviously it can never be used as a wallet. So how did I make such a mistake in dream?

Certainly our reasoning ability is limited in dream, though this time the problem seems to be related with memory solely. There is saying (Fruedian?) goes that the memory in dream is actually distorted. But I concern, at least for my case, the memory in dream was fake instead of just distorted. That is, I can not access parts of my memory while I was dreaming.

Finally, no matter the memory is distorted or fake, the mechanism of the distortion or falsification needs to be studied, not just the concepts.

Or go further: how can we know our memory is right for certain, without any distortion or falsification?