I can appreciate your worries about interference between various wireless devices. However, what you experienced is most likely due to the very reason you've already stated yourself - a lot of this kit is manufactured in the far east, and clearly, little effort has gone into R&D in terms of interference mitigation.
It's more likely to be a fault in the design of the doorbell than anything else. The energy monitor has to transmit a data stream to the receiver, so there will (hopefully) be some basic error checking and addressing going on there to allow them to talk to each other. As the doorbell only requires an 'on' signal from the bell push, it probably just transmits that signal on a certain carrier frequency, with no validation at the receiver - ergo, anything operating on that frequency can cause the doorbell to go off.
Although bad design, it's not really a problem for insecure devices. The protocols used by wireless keyfobs for cars, alarms, garage door openers and the like are more secure. Admittedly it's not really my area of expertise, but I believe they rely on a system whereby a the receiving device stores a master cypher, which the user can then program into the transmitting devices they use with the system. As only the receiving and transmitting devices know the cypher, it is very difficult (but not impossible) for anyone to decrypt the signal over-the-air.
None of these should cause problems with life-saving devices (although I'm not sure to exactly what you're referring) if properly designed. What you're talking about now is Electro Magnetic Compatibility, which refers to the electromagnetic waves generated by almost all modern electronics, regardless of whether or not they intentionally incorporate any kind of transmitter. I believe EMC testing is a requirement to gain a CE mark, so most any device you buy in this country should be guaranteed to operate in harmony with other electrical devices around it.
Sometimes it's unavoidable that some spurious interference will be generated (like when using a mobile phone near a radio, or running a large motor), but manufacturers should make some effort to minimise the susceptibility of their products to electromagnetic interference, as well as to limit the generation of it. One would hope that medical devices would be properly shielded such as to prevent this kind of interference, given how commonplace it actually is.
I wouldn't worry yourself too much about digital TV signals. High power transmitters have been around us for a long time, but the truth is that at distance, the EIRP (that is, Effective Isotropic Radiated Power) is not very high at all, as the signal is spread out over such a large area. If this sort of thing does worry you then you should be far more concerned about using mobile phones, which can and do generated EIRPs in short bursts of up to 1 watt, and we're (well, most of us) quite happy to put them up against our head.