Q:

use RFID remotely

From the answers to this question it's clear that RFID is passive and (therefore) doesn't work in the far field.
I was wondering if you couldn't use it remotely if you make an actual transmitter of the tag, sending a 125kHz carrier AM modulated with the tag's code. Wouldn't the reader pick up this signal?  
edit Olin Lathrop mentioned one wavelength as a rule of thumb for the limit of the near field. But at 125kHz this is 2400m! Is the rule of thumb still valid for these low frequencies?

A:

You can certainly transmit 125 kHz with a signal on it, but most likely this won't be picked up as you expect by the reader.
The details depend on the exact reader design.  The few I've seen the inner workings of didn't look at signal strength in their vicinity because they were always transmitting.  They looked for changes in load on the transmitter.  Basically the change in load was high pass filtered, then that signal attempted to be interpreted as the expected digital data stream.  The tag sends its signal by varying the load on its receiving coil.  As you can imagine, lots of things can go wrong with this so there are lots of retries and CRC checksums on each message.
I've heard some fancy readers modulate the outgoing field to encode a challenge number.  The tag hashes this with its stored internal unique number and responds with the result.  That prevents someone from easily copying a tag by getting it to dump its ID once.  However, these kinds of systems are much rarer and I've never seen the details of such a reader.
In both cases as far as I know, the reader is looking for varying load on its antenna, which is basically a coil.  Another outside signal at the same frequency would interfere contructively or destructively, depending on what the phase relationship happened to be.  It's possible that the destructive interference could look like a higher load, but I've never tried that nor heard of anyone trying that.  If you get the carrier phase wrong, I suppose the bits would look inverted, which probably would not be a valid message.
All in all I don't think this will work very well, if at all.

