Bash tab completion for command called by time

Question

A custom command based (complete -C ...) completion works fine when invoked from the top level. Like

my-command <Tab>

Completion code

package main

import "fmt"

func main() {
    fmt.Println("foo")
}

The completion command is provided with 3 arguments - completed command name, current word and previous word - and 4 envirnoment variables - COMP_KEY, COMP_LINE, COMP_POINT, COMP_TYPE - as described in documentation chapter Programmable Completion Builtins.

However when invoked with time prefix (to measure execution time), like

time my-command <Tab>

the completion command is invoked without COMP_LINE and COMP_POINT environment variables set and arguments are set to compget, current word and empty string. Also warning

bash: compgen: warning: -C option may not work as you expect

is printed.

I have 2 questions

• Is the changed way the completion command is called result of insufficient implementation of completion for time command, or general limitation of command based completion (complete -C)?
• How to make it work? How to get rid of the warning and get necessary state data from the completion command - at least a string of line being completed and current cursor position?