My "Windsor" branded AM-FM clock radio has about the worst tuner and audio quality I have ever heard, but it doesn't bother me since all I use it for is to make noise to wake me up in the morning. The selectivity is so bad that the local stations from Cleveland come in almost one on top of the other; a station about ten miles from here is so strong it almost drowns out a Cleveland station one MHz up the dial, but again, that's due to the poor selectivity factor.
As was mentioned earlier in the thread, these radios are not meant for high fidelity or razor-sharp selectivity, much less good RF sensitivity. However, I have owned worse sets. In the eighties, I had a Zenith integrated stereo with an AM tuner so bad I was getting short wave around 1110 kHz or so after dark, and my present stereo system, an Aiwa NSX-888 all-in-one, will pick up the local AM station, 1000 watts days/500 watts nights and five miles from me, at two points on the digital tuner: at the station's primary frequency of 1460 kHz, and 0.9 to 1 MHz down the dial (at 550-560 kHz) as well. (That station is a talk station I do not listen to, so the cross-modulation problem doesn't bother me.)
I wouldn't expect such a low-power station to overload my stereo's front end at just five miles, but the way these things are built nowadays nothing surprises me anymore. The FM digital tuner is just the opposite, failing to receive certain Cleveland stations in stereo, but I'm not surprised. Some time ago, I read one review of this particular system that stated the FM tuner is meant for use in strong signal areas, not in near-fringe areas such as the town where I live (I am about 40 miles northeast of most of the Cleveland FM stations, so the signals here aren't that strong to begin with). In fact, extremely strong signals will likely overload the front end, resulting in the same type of cross-modulation I mentioned earlier; you just can't win.
This type of stereo system would probably overload like crazy if I lived in a very strong signal area such as New York City or downtown Chicago, as most of the radio stations serving these areas transmit from one central location (the Hancock Building in Chicago and the Empire State Building in NYC) and, of course, the signals are extremely strong in the downtown areas of both cities. If you are close to either of these structures your radios will overload severely. VK member jstout66, in Nebraska, can relate to this as he has a 50kW AM station near his home that almost certainly overloads every radio he owns.
TV signals in both areas are likely just as strong, as they are transmitted from the same towers as the radio stations. In the early 1970s, I lived in a Cleveland suburb whose local FM station was only roughly a third of a mile from me (I could see the tower and its red navigation lights from my third-floor bedroom window after dark). The station's signal, on 92.3 MHz, was so powerful that it came in on channel 6 on my TV, between stations on a cheap stereo FM radio I had at the time, and even on an Ampex "Micro 88" solid-state stereo cassette tape deck my dad had. He was trying to tape a concert at our church one night, but couldn't due to the tape deck picking up the FM station's signal on the speaker leads; this gives you an idea of how incredibly strong the signal was at that location.