<Can = I assert that it is possible that ...
Could = I assert that it is "remotely" possible that ...

I don't think that "assert" fits very well here because 'can/could' can be epistemically very weak. This is especially notable in speech where intonation strengthens or weakens 'can/could'.

That caaaaaan happen. OR That cooooould happen.

Also, while 'could' is used to discuss remote/impossible events, it can also be used as a near equivalent of 'can'. >

Is that to reply to an assetion? "That" is anaphoric, so something must have been asserted rearlier by another speaker. The use of can there is not being used in its basic semantic meaning, but either shows, doubt, support, or signals new, or contradictory information is to follow. That's why intonation is being used- to weaken or stengthen the original assertion.

Example:

It can snow even in high summer here.

That can happen, but it hasn't snowed for at least ten years at that time of year.
.............

It can snow even in high summer here.

Yes, that can happen, and it can go on for days.