I personally would think low budget is sort of an opinion. Someone who likes to see lots of explosions and fire and things being blown up might consider anything without those to be low budget. Someone else might think that a badly acted and/or directed movie is low budget.
I personally think there is no real low budget look. To me, low budget doesn't mean bad quality or anything less of a movie, it simply means a challenge to get their production costs within their constraints! It's a different kind of movie than the multi-million dollar Hollywood blockbusters.
Now what makes a film look ameteur or professional is a different story.
If I had to guess, you friends might of thought of Primer as low budget because of a few key aspects of the film? For example, many of the shots didn't involve a lot of camera movement was fairly static (I admit that it's been a while since I last watched it, so I can't remember how much was static and how much had movement). Also, they used old laptops and old computer equipment while there were papers that showed it was in the mid 2000's. The director actually commented on the props saying that they did this to help create a timeless atmosphere. They didn't want to tie it down to anyone time (although this is debated).
I'm interested in hearing more about what you and your friends were thinking. It might be fun to start a discussion about qualities of good movies, bad movies, low budget, high budget, and how people have found balances to make good movies regardless of the budget (btw, Primer
was low budget at about $7000 which was mostly spent on film processing

).