Reported speech - "He said he likes you." vs "He said he liked you."

The general rule of reported speech is that we place what the person said into the past form, i,e. "I like her." to "He said he liked her."

However, surely "He said he likes her." is not grammatically wrong. The speaker has indicated that this is something said in the past by saying "said" but is indicating their statement is still currently true by using the present verb, "likes", meaning they believe / know the person who they are talking about still feels this way. If you say "liked" it can possibly indicate you are unsure or the statement was once true but no longer true.

Another example:

"Does Tim like ice-cream?

"Yes, he said he liked ice-cream."

"Yes, he likes ice-cream."

Which of the last two sounds like the speaker is more sure of their answer? I'd argue it is the last one. When you report purely in the past tense, it sounds like you're unsure.