How did my TV capture neighbour's DVD player's frequency?
It's hard to be sure what was going on without knowing the exact physical setup and equipment used but random speculation and guessing is always possible.

I'm assuming this was a fairly old DVD (or possibly VHS?) player that had an RF output that allowed you to connect via the antenna input to the TV rather than using composite video, HDMI or some other connection system. Modern players don't have this output because it's lower quality and all newer TVs have other options to connecting but some older players did have it.

Clearly the signal was leaking from their DVD player into your TV. A DVD player is going to output a fairly strong signal, the manufacturers don't want complaints and returns because a customer used a long or low quality cable so they will output towards the upper end of the signal strength range that TVs are designed for. 
If they weren't using the RF output from the player then the unconnected socket on the back will act as a transmitting antenna. It won't work very well but some signal will get out.

A TV is designed to pick up signals over a very wide range of signal strengths, when you are dealing with radio signals the signal strengths can easily vary by factors of thousands or more. This means that they can pick up some very weak signals, especially if the antenna is pointing roughly at the signal source. If things were physically close enough then your TV could have picked up the signal leaking out of the back of their player.