I'd like to make some comments on capacitor specifications:
As far as capacity (uF) goes, you want to duplicate that if possible but electrolytic caps aren't terribly precise components, usually +/-20%. There is an industry standard that sets out capacity values so you won't encounter too many "odd" values in a typical circuit. If I was stuck, I wouldn't hesitate to try the next larger size to replace an electrolytic cap.
The voltage value marked on a capacitor is a "maximum working voltage". Therefore, if a cap is spec'd at 10v and you expose it to a voltage that's higher or even near its rated voltage it's liable to fail, sometimes visibly, sometimes not. Bulging seems to be the common symptom here but they can also leak, sometimes under the cap itself where you won't see it.
Typically with components that have a maximum value that they can withstand, usually current or voltage, you want to derate them by 50% when designing a circuit. If you had a circuit where the capacitor will be exposed to as much as 10V, you would ideally use a cap rated at 20V. You could use a 50V cap or anything higher - it wouldn't make a bit of difference other than the cost.
So the question is, what is Bell/Dish/whoever doing wrong, at least from the consumer's point of view? They're using cheap caps, not derating the voltage properly, or both. I think we'd all guess the latter. Perhaps they're using 6.3V caps on a 5V circuit. Yes, it's enough to keep the box from blowing up when you plug it in, but eventually you're liable to see a failure. Or the caps could be derated properly but are just junk.
The manufacturing cost to step up the voltage rating is probably minimial but I'm sure they've calculated the savings in making most of their boxes work just long enough for the warranty to expire.
Obviously we don't know what voltages these caps are exposed to, so if you're replacing them, step the voltage up on the replacements, again about 2x the original. We can probably assume the replacement caps are of better quality and if they're rated at a higher voltage then you've covered all the bases.
The last thing you have to look at is size - will the replacement fit where it has to go? When you're installing them, note that they do have a + and a - terminal and shouldn't be installed backwards.
Electrolytics don't like heat either but there's not much we can do about that other than keeping the fan working, adding additional cooling, or running the box with the lid off.
I hope this helps.