Here is definition 2c for "can" on freedictionary.com:

Used to indicate probability or possibility under the specified circumstances: "They can hardly have intended to do that."

I am a native speaker and I have asked myself this same question a few times when I have heard it; in fact, I just heard it a few days ago on an old television show from 1968 and every time I hear it on television, which is very rare, I flinch. The character said:

"He can't have gone far."

I personally disagree with the construction and would never say it since "could" is the past tense of "can" and this statement is talking about the past, i.e

"He left ten minutes ago, so he couldn't have gone far."

I suppose the question is whether it is grammatical. My answer is that I don't know; I've heard it before, but it doesn't make sense grammatically and it's rare to hear it or see it in writing. Would I use it? Never. I refuse to use something that is awkward like that when "could" works even better. It's your choice though. It's more heard when it's in the negative and "They can hardly have intended to do that" has a negative meaning.

I hope somebody else can answer this question better than I can. I'd appreciate a definitive answer.

Here is definition 2c for "can" on freedictionary.com:

Used to indicate probability or possibility under the specified circumstances: "They can hardly have intended to do that."

I am a native speaker and I have asked myself this same question a few times when I have heard it; in fact, I just heard it a few days ago on an old television show from 1968 and every time I hear it on television, which is very rare, I flinch. The character said:

"He can't have gone far."

I personally disagree with the construction and would never say it since "could" is the past tense of "can" and this statement is talking about the past, i.e

"He left ten minutes ago, so he couldn't have gone far."

I suppose the question is whether it is grammatical. My answer is that I don't know; I've heard it before, but it doesn't make sense grammatically and it's rare to hear it or see it in writing. Would I use it? Never. I refuse to use something that is awkward like that when "could" works even better. It's your choice though. It's more heard when it's in the negative and "They can hardly have intended to do that" has a negative meaning.

I hope somebody else can answer this question better than I can. I'd appreciate a definitive answer.