Can bailiffs take control of goods then make me prove they're not the debtors?

No

Bailiff may only take control of goods that belong to the debtor.^[1]

If a bailiff takes control of goods that do not belong to the debtor, the owner can make a third-party claim to controlled goods.^[2][3]

Bailiffs must exercise caution to minimise the risk of taking control of another person's goods, because the third-party claimant to controlled goods may apply for costs,^[4][5][6] together with damages,^[7] which can be substantial, if the court is shown the bailiffs behaviour has been unreasonable.

An example of unreasonable behaviour is a bailiff taking control of goods of another to coerce the owner to "voluntarily" pay a debt on behalf of the debtor.^[8]

^{[1] Paragraph 10 of Schedule 12 of the Tribunals, Courts and Enforcement Act 2007
[2] Civil Procedure Rule 85.4
[3] See Making a third-party claim to controlled goods
[4] Civil Procedure Rule 46.5
[5] Practice Direction 46.5 Rule 3.1
[6] Civil Procedure Rule 44.2
[7] Section 3 of the Torts (Interference with Goods) Act 1977
[8] See Bailiff wrote on a document you paid a debt voluntarily}