Do you need a free hand for your holy symbol if you’re wearing it visibly?

I’ve been creating a Paladin who uses the Defense fighting style while wielding two weapons (instead of the more common Dueling style with weapon and shield). However, I was worried that spell components would make this too difficult because the character wouldn’t be able to use a shield emblazoned with a holy symbol as their spellcasting focus. However, I reread the section on holy symbols and it says the following:

A cleric or paladin can use a holy symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, wear it visibly, or bear it on a shield. [PHB pg. 151, emphasis added]

By my reading of this, even absent a shield, the caster does NOT need a free hand for their focus. Simply wearing it on a chain outside their armor or clothing (or even affixing it to the outside of their armor) would be sufficient.

This surprised me, so I double-checked the material components section:

Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell… A spellcaster must have a hand free to access these components, but it can be the same hand that he or she uses to perform somatic components. [PHB pg. 203]

At first glance, its seems that the statements "A character can use… a spellcasting focus… in place of the components specified for a spell" and "A spellcaster must have a hand free to access these components" would logically mean that a spellcaster must have a hand free to use a spellcasting focus.

However, is this a case of "specific beats general"? Using an arcane focus requires a free hand because it follows the general rule from pg. 203, but a holy symbol doesn’t as long as it’s visibly worn as written in the more specific rule on pg. 151?

(Related: Do these spellcasting foci from Xanathar’s Guide to Everything have to be held in a hand?)