There are two basic types of UPS, backup and online. An online UPS takes AC line current and converts it to DC for charging and maintaining the battery. Coming from the battery is an inverter that turns the DC from the battery into AC. A standby UPS does essentially the same thing, but the inverter stays turned off unless the power goes out completely. Otherwise the AC input to the UPS goes straight to the output outlets.
While an online UPS doesn't need to do anything to supply power to the load if AC line power is lost, the standby UPS must figure out when the power is out so it can turn on the inverter. It can't use something simple like zero voltage to start the inverter because 60Hz AC is at zero volts 120 times a second. The only reliable way is to wait to start the inverter after the voltage is zero for a certain amount of time. So a standby UPS always has some delay between losing AC line power and getting the inverter started up.
Most home wiring uses a system called split-phase. Split phase is a single phase system that is able to get two voltages by using a center tap neutral wire that gives half the voltage between neutral that exists between the two live wires. Most of your home wiring uses the lower voltage between the neutral and one or the other hot wire.
Most people don't think about AC wiring having resistance, but the fact is that everything has some resistance. Even superconductors aren't 100% efficient. With split-phase, this becomes a problem when more current flows between one hot and the neutral than does with the other hot wire. This results in having a voltage potential on the neutral wire. It's this voltage that causes audio buzzing and sometimes a nasty shock. The latter is why a ground wire is also used in many appliances.
So if the receiver is on the same leg as your UPS, Ohm's Law tells us that the high current and wire resistance will cause a voltage drop. And since the other leg is actually part of the same circuit, it will also be affected.
Interestingly enough, by unplugging the TiVo from the UPS and plugging it directly into the wall has alleviated the problem for now. I had originally purchased the UPS to keep the TiVo (and tuning adapter) from restarting during those annoying summertime thunderstorms where the lights will flicker occasionally.
The primary function of any UPS is to provide some form of power to the load when the utility power quits. Although some UPS makers claim that their products provide AC voltage regulation, surge protection or power conditioning, it's likely to be a very inexpensive afterthought if anything at all. A standby UPS isn't a very good choice if your lights just flicker.
Flickering lights are most often caused by wind, which can move overhead power distribution wires enough to make less than solid connections become intermittent. That's if you're lucky. Eventually the loose connection will break, and the result can be as damaging as a lightning strike.
Speaking of lightning, that's the other most likely source of problems. If your lights are just flickering and not all dying right after one brilliant flash, the lightning is probably far away. Power substations and generating facilities have sophisticated equipment protecting their facilities. When activated, they essentially turn off parts of the power grid, which is what makes the lights flicker.
Flickering lights mean you got lucky...this time. If you want your equipment to survive more serious power faults, invest in a serious power protection system. The best one that I know of is disconnecting all sensitive equipment for as long as there's a weather threat. That's fine when you're going to be home the whole time and have nothing to record. I use Brick Wall protectors, which can dissipate a 18 megawatt surge every minute for 1000 minutes (nearly 17 hours). This is based on IEEE standards for worst possible indoor conditions.
When it comes to a UPS, an online type would be best. There are long run time models, but they're expensive. So instead I use a regular 1000-1500 kVA UPS to power my DISH box, 2 HD TiVos and the TV. Even with a fairly large UPS I only get 30 minutes or so of run time. So the TV is needed to do an orderly shutdown if necessary.