Is "recent past" an oxymoron?

I saw "recent past" included in a page of supposed oxymorons posted on Facebook, with people yukking it up while apparently badly misunderstanding what an oxymoron is. One well-meaning but confused gentleman pointed me to a link to a different page also claiming that "recent past" is an oxymoron.

This seems ultra-simple to me: the two words have to be in apparent conflict, but they're simply not. I tried to give a helpful example (having gone to the store yesterday) but think the people arguing with me may still not understand.

Am I wrong?

No. You are correct. It is both common and acceptable to qualify the past as the distant past or the recent past.

You are correct about usage: it is not an oxymoron, because "recent" and "past" are not in opposition. The word "past" in that phrase is, to an extent, redundant. An oxymoron would be an instance of two words whose meanings suggest each other's opposite, or at least significantly dissimilar concepts. As a comment suggests, a phrase containing some redundancy such as "recent past" might be called a pleonasm, though I don't think it's a common term in regular conversation.