On Healing - Tim

I thought that something Tim said in his message on Sunday was pretty interesting, talking of the healing of the lame man in Acts 3 he said;

"Now it’s important to see here that it is not the lame man here exercising faith because verse 5 says he just expected to receive something (money) from them.
There is no reason in the text to think he was believing when Peter spoke to him.

Every time there is a healing in the book of Acts, it is unbelievers who are healed (3:1-11; 5:15-16; 8:7; 9:33-34; 19:11-12; 28:8).

The scriptures that deal with Christians who are sick would support the view that the gift of healing was not used on behalf of the church.

Paul did not heal Trophimus but left him sick at Miletus (2 Tim. 4:20).
Nor did he advise Timothy to go the local healer for his medical problems – he told him to take a little wine for his illness (1 Tim. 5:23).

Does this mean that God doesn’t heal people today??

Of course not! God may choose to heal today in response to the prayers of his people, when that is consistent with His will."