How can I tell the difference between theory and proven fact?

A fact is something observed or recorded: a meeting took place on this date; this company holds this stake. An inference is a reasonable conclusion drawn from facts. A hypothesis is a proposed explanation awaiting testing. Speculation is a possibility with no supporting evidence yet.

All four are legitimate. Problems start when speculation is presented in the grammar of fact.

'Records show' is different from 'sources suggest', which is different from 'many believe' and from 'it is obvious that'. Each signals a different level of support, and careful writers choose deliberately.

When a piece slides from documented verbs to rhetorical ones, note the sentence where it happens. That is usually where the evidence stopped.

Outside mathematics, almost nothing is proven absolutely. Courts use standards of proof; science uses replication and convergence. Both reward accumulated independent evidence over any single dramatic item.

'Well established' is the realistic top of the scale, and it is a strong position.

Take any article and mark each claim as fact, inference, hypothesis or speculation. Count them. You will often find one fact carrying twenty inferences, which tells you how much weight the argument is asking a single item to bear.

Do this to writing you agree with as well. That is the part that improves your judgement.

Marking your own uncertainty out loud is a discipline, not an admission of weakness. It is also the fastest way to be trusted by people who can tell the difference.