This is a great example of how poor modern AM radios are.
At 770, there should be no response from a signal on 880, even 50kw.
I've seen and had to use such radios in rentals and such, but I'm not going to easily give up
the performance of my old Bendix and Motorola AMs.
Unless there are some other "nearby" signals which could create an "image", this shouldn't be audible.
A return to the 1930s rf performance of mushy autodynes is no progress and not acceptable.
You have experienced the phonomena known as "walking through".
Proper shielding and other design features would have prevented it.
Supposing you were listening to an actual signal on 770, it would be an ugly mess.
This is no reason to not be able to expect to listent to a signal 100 khz offset.
WGN, WBBM and WSCR in Chicago have a little "fun zone" in the nearby region that gives modern car radios fits.
Especially if they happen to be trying to listen to 890 WLS, 35 miles south.
Many radios just swamp out on 670,720,780 signal and 890 becomes inaudible.