Reverse Doppler Effect?

In regard to the page: http://seticlassic.ssl.berkeley.edu/about_seti/about_seti_at_home_4.html

Specifically,
The Doppler Effect part...
"Because planets rotate, both the extraterrestial transmitter and our telescope are movin in circular paths around the axis of their planet. This motion shows up as a changing relative speed during the course of the observation. Because of this, there is likely to be a "doppler shifting" or changing frequency, of the signal because of our relative motions. This might cause the signal to rise or fall in frequency slightly over the 12 seconds. These are called "chirped" signals. We'll check for this too."

"Let's look first at the most computationally intensive portion of the calculation. The first job is to "de-chirp" the data - that is, to remove all the effects of the doppler acceleration."

What if the ET's are expecting The Doppler Effect, and so are compensating for it; thus, in "De-Doppler-izing", in effect, we are Scrambling the message? Of course, this would only result in a ... something like a negative image (like a photograph), or a reversal, of what The Doppler Effect would be, and so can be easily corrected for.

However, if we're not looking for this possibility, might we be ignoring a huge potential source of data? What if we're scrambling it, not realizing so, and so will be unable to see what was sent because of that?

Or have I missed something obvious? I'm thinking I have...

Thank you.