It's hard to prove a negative. But perhaps we can find some evidence.
Documentation
From the documentation, at https://ola.hallengren.com/sql-server-index-and-statistics-maintenance.html:
An online index rebuild or an index reorganization is not always possible. Because of this, you can specify multiple index-maintenance operations for each fragmentation group. These operations are prioritized from left to right: If the first operation is supported for the index, then that operation is used; if the first operation is not supported, then the second operation is used (if supported), and so on. If none of the specified operations are supported for an index, then that index is not maintained.
That documentation -- found under the FragmentationLow, FragmentationMedium, and FragmentationHigh parameters -- agrees with your recollection, and the first part of your friend's assertion. If Ola's index maintenance script retried by going to the next option if an attempt failed, this would be where I would expect to find it documented.
Code
From the downloadable IndexOptimize.sql, which creates the IndexOptimize stored procedure:
In the section that begins with the comment of "Which actions are allowed?", we find a number of checks to see which of the INDEX_REORGANIZE, INDEX_REBUILD_ONLINE, and INDEX_REBUILD_OFFLINE are allowed. Those checks include, but are not limited to, the SQL Version, the Engine Edition, and the current index type. It then picks which of those actions to use, builds the command, and executes the command, with a line like this:
EXECUTE @CurrentCommandOutput = dbo.CommandExecute @DatabaseContext = @CurrentDatabaseName, @Command = @CurrentCommand, ...
It then checks for an error, and sets the return code.
SET @Error = @@ERROR
IF @Error <> 0 SET @CurrentCommandOutput = @Error
IF @CurrentCommandOutput <> 0 SET @ReturnCode = @CurrentCommandOutput
That's pretty much it. Nothing about a retry. There are a few places in the procedure that use the Try/Catch syntax, but not around the index rebuilding actions.
Verdict
Your recollection is correct. Your friend's assertion -- that if the reindexing operation runs into an error, it will retry using the next thing in the list -- is not supported by the evidence.