Why is "established facts" better than "established truth"?

This is a question of how English normally uses these words, not merely grammar.

What is a fact?

A fact is something that can be supported or verified by evidence.

Examples:

The Earth orbits the Sun.

Water boils at 100°C under standard atmospheric pressure.

These are facts because evidence supports them.

Therefore English naturally says:

• establish a fact
• prove a fact
• verify a fact
• document a fact

These combinations are extremely common.

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What is truth?

Truth is a much broader philosophical idea.

Truth may refer to:

• objective reality
• moral truth
• religious truth
• personal truth
• emotional truth
• artistic truth

For example:

Justice is an important truth.

Love reveals profound truths about human nature.

These are not "facts" in the scientific sense.