Led Zeppelin never toured with any musicians in the band other than John Bonham, John Paul Jones, Jimmy Page and Robert Plant, up until Bonham's death in 1980.
In their reunion concerts in the most recent decade, they performed with John Bonham's son Jason Bonham on drums.
Led Zeppelin only made two public appearances, officially under the name Led Zeppelin, that were not part of tours. The first was a single appearance at the Live Aid festival in London in 1985, where Jimmy Page, Robert Plant and John Paul Jones were joined by Phil Collins and Tony Thompson on drums and Paul Martinez on bass guitar.
The second public appearance under the name of Led Zeppelin was the 2007 concert to honor the death of Ahmet Ertegun, and the lineup for that concert was Jason Bonham, John Paul Jones, Jimmy Page and Robert Plant.
In short, this person you met in church must have been lying to you. He never performed with Led Zeppelin.
However, since 1980, the three surviving members of Led Zeppelin have performed as solo artists and as members of various different bands, never under the name of Led Zeppelin, but at various times they would perform certain Led Zeppelin songs as part of their concerts. So it may be possible that this person you met has performed with a former member of Led Zeppelin on a tour at some point in time. Yet I am certain that this could not have happened under the name "Led Zeppelin". This is just too well-documented.
Similarly, ZZ Top has never performed with any guitarist other than or in addition to Billy Gibbons, their founder. ZZ Top in live performance and tours has only ever consisted of the trio of Billy Gibbons, Dusty Hill and Frank Beard. They have never made use of any other musicians within that band in live performance. If this person told you that he had performed as a touring band member in ZZ Top, he was lying.
Occasionally in the world of rock and roll you find people who tell tall tales and lies about their experiences as a musician. Maybe this person played in a little-known band at a festival where there were 16 bands and one of the headliners was ZZ Top. In later years this person would claim, "Yeah, I played with ZZ Top" when all he meant was that his forgotten band was on some different stage in the festival on a day when ZZ Top were not even there.
But for him to claim that he performed as a member of Led Zeppelin or ZZ Top is particularly egregious; everybody knows that Led Zeppelin only ever toured as a four-piece, and ZZ Top only ever toured as a trio, and we know who each of those members was.