It's because of the thickness and the type of metal, as well as the signal type.

EDIT: NOTE: Upon further thought it needs to be stated here that various different metals have very excitocally different noise rejection curves, so generally copper or aliminium may not be better in all cases, they may even be worse. The central point to the answer remains largely in tact, though.

If your tin were made of copper or aluminium it's very possible AM would have been reduced enough to be unusable, but the tin is made of a less conductive alloy than either of those, so it has a harder time keeping out the waves.

The higher the wave frequency is, the thinner the metal sheet can be to keep it out/reflect it.

Apart from that, an AM signal is a wave that is stronger and weaker in the frequency of the sound. AM stands for Amplitude Modulated/Modulation. So the signal gets weaker and stronger to identify the audio wave. Because that system is very sensitive to the signal strength to supply audio, there's an auto-gain control on it, that tries to amplify it.

So there is some signal left, because the tin isn't a great conductor and just about thin enough to let some AM frequencies through, and then the Auto-Gain tries to make something of it by amplifying it till it makes some semblance of the original audio.

It's because of the thickness and the type of metal, as well as the signal type.

EDIT: NOTE: Upon further thought it needs to be stated here that various different metals have very excitocally different noise rejection curves, so generally copper or aliminium may not be better in all cases, they may even be worse. The central point to the answer remains largely in tact, though.

If your tin were made of copper or aluminium it's possible AM would have been reduced enough to be unusable, but the tin is made of a specific type of alloy that may or may not be working as well as a shield. (As per the comments, it turns out it may be better, but that doesn't change the remaining point:)

The higher the wave frequency is, the thinner the metal sheet can be to keep it out/reflect it. This comes from EM-field theory, but within usable parameters it is generally true that a thinner sheet of metal will work better for high frequencies than low frequencies. The thickness then defines at what frequency you "stop hearing" anything. There are some exceptions for hair-thin sheets and certain types of waves or frequencies, but you can ignore those for now.

Apart from that, an AM signal is a wave that is stronger and weaker in the frequency of the sound. AM stands for Amplitude Modulated/Modulation. So the signal gets weaker and stronger to identify the audio wave. Because that system is very sensitive to the signal strength to supply audio, there's an auto-gain control on it, that tries to amplify it.

So there is some signal left, because the tin is just about thin enough to let some AM frequencies through, and then the Auto-Gain tries to make something of it by amplifying it till it makes some semblance of the original audio.

As an experiment you could try wrapping the radio (in a plastic bag, so you can't accidentally cheat by modifying the antenna) in thin tinfoil, or other thicker and thinner metals and see which waves stop working when.

It's because of the thickness and the type of metal, as well as the signal type.

If your tin were made of copper or aluminium it's very possible AM would have been reduced enough to be unusable, but the tin is made of a less conductive alloy than either of those, so it has a harder time keeping out the waves.

The higher the wave frequency is, the thinner the metal sheet can be to keep it out/reflect it.

Apart from that, an AM signal is a wave that is stronger and weaker in the frequency of the sound. AM stands for Amplitude Modulated/Modulation. So the signal gets weaker and stronger to identify the audio wave. Because that system is very sensitive to the signal strength to supply audio, there's an auto-gain control on it, that tries to amplify it.

So there is some signal left, because the tin isn't a great conductor and just about thin enough to let some AM frequencies through, and then the Auto-Gain tries to make something of it by amplifying it till it makes some semblance of the original audio.

It's because of the thickness and the type of metal, as well as the signal type.

EDIT: NOTE: Upon further thought it needs to be stated here that various different metals have very excitocally different noise rejection curves, so generally copper or aliminium may not be better in all cases, they may even be worse. The central point to the answer remains largely in tact, though.

If your tin were made of copper or aluminium it's very possible AM would have been reduced enough to be unusable, but the tin is made of a less conductive alloy than either of those, so it has a harder time keeping out the waves.

The higher the wave frequency is, the thinner the metal sheet can be to keep it out/reflect it.

Apart from that, an AM signal is a wave that is stronger and weaker in the frequency of the sound. AM stands for Amplitude Modulated/Modulation. So the signal gets weaker and stronger to identify the audio wave. Because that system is very sensitive to the signal strength to supply audio, there's an auto-gain control on it, that tries to amplify it.

So there is some signal left, because the tin isn't a great conductor and just about thin enough to let some AM frequencies through, and then the Auto-Gain tries to make something of it by amplifying it till it makes some semblance of the original audio.