Both of your friends are right, because it depends on the context.
First we have to understand why you would want to say this. The most common context would be in response to a question, phrased in the progressive because the person asking the question is thinking of some event that was happening at the same time.
A: What were you doing at 7pm last night?
Your answer should also be in the progressive:
B: I was watching television at 7pm. Why?
The related event could be explained using the simple past:
A: Because I texted you at 7pm to see if you wanted to meet us at the pub, and you didn't respond.
Or, if it was an ongoing event, the progressive:
A: Because everyone was having drinks at the pub at that time, and I texted to see if you wanted to meet us.
Although it's grammatical, it's a little strange to just say "I watched TV at 7pm last night". It's hard to think of a situation where the simple past makes sense, because watching television is an ongoing activity, that you were doing for some period of time around 7pm.
I suppose we could use our imagination -- for example, suppose you are being questioned by the police:
Police: Now sir, what did you do last night around 7pm?
You: I watched TV at 7pm last night.
Police: And how do you know the exact time?
You: Because my favorite show comes on at 7pm. I always watch TV at 7pm, every night.
Because the police officer's question is phrased in the simple past, you might choose to respond with the simple past. You don't have to -- you could rephrase to the progressive if that makes more sense for an ongoing activity, especially in relation to some other event.
Police: Now sir, what did you do last night around 7pm?
You: I was watching TV from 6 to 9 last night, so I couldn't have been robbing that bank.
Again, this is more about the idiomatic way people say things in English, rather than simple grammar. It might be different with a different verb. For example, if you were talking about something that was not an ongoing event:
I ate dinner at 7pm last night
Obviously you didn't eat your entire dinner in that moment, but it's idiomatic for English speakers to talk about when a meal begins rather than how long it takes. You could use the progressive if you wanted to relate it to another event at the same time:
I was eating dinner at 7pm last night, so I couldn't have been robbing that bank.