"At this time" vs "At that time"

Is it acceptable to use "at this time" when referring to a specific point in time in the past? While in the process of telling a story, for example, that happens completely in the past?

To me it just does not sound right, and I used to correct a non-native speaker (even though I am one also, only more advanced). Since then, however, I have heard it a couple of times (I'm in the USA).

EDIT

After receiving couple of answers confirming my view, I would like to give a specific example I just found of that "incorrect" (I think) usage in this Wikipedia article on the Holy Roman Empire. (Please do a search in the text there for "at this time.")

"This" and "that", much like their counterparts in most other European languages, indicate relative proximity. "This" refers to a thing that is literally or figuratively "here", as in "within reach" of the person. "That" refers to a thing that is literally or figuratively further away, but "within view". "At this time" is thus normally used when referring to the present time, and "at that time" is used when referring to specific past or future times.

HOWEVER, "this" can also be used to refer to something being discussed in the present context, even if the subject of the discussion is far away in place or time. "At this point in time" or simply "at this time", then, could be used to refer to the particular point in time that is central to the discussion. Similarly, one could point at something they're holding in their hand and refer to it as "that". So, more generally, "this" is something central and implicit in the statement; "that" by contrast is something more separate or which must be identified by location or time.

When telling a story, I (a native American English speaker) would most likely say "at the time". For example, if I were telling someone else about my day I might say:

When I was little, I went to school 6 days a week. At the time I thought it was brutal, but it was actually beneficial to my education.

At this time to me refers more to a scenario in the present. It is used more in announcements or on signs, for example:

Commenting is not available at this time.

There is some discussion about this phrase in a blog here.

Finally, at that time is very similar to at the time. It refers to a very particular point in the past. A sample sentence where I might say it would be:

Four years ago, I broke my leg. At that time, I thought it was the end of the world.