This myth again. Let's look at some matches.
1.
5th Match: Australia v India at Brisbane, Jan 18, 2004 | Cricket Scorecard | ESPN Cricinfo
Bevan comes in at 7 with Aussie needing 100 off 16 overs. An absolute doddle, you'd think, for a master like Bevan, but he fails to even score at a run a ball, hitting a pitiful 3 boundaries from 43 balls, and Aussie run out of wickets, losing by 19 runs.
2.
2nd ODI: Australia v Pakistan at Melbourne (Docklands), Jun 15, 2002 | Cricket Scorecard | ESPN Cricinfo
Batting at 6, Bevan limps to 30 runs off 52 balls, scoring one solitary boundary in a one and a half hour long innings. Thanks to chasing such a low score Pakistan win with 2 wickets to spare. Probably would have been a win for Aussie if Bevan could have managed so much as a SR of 80 here.
3.
4th Match: Australia v New Zealand at Sydney, Jan 17, 2002 | Cricket Scorecard | ESPN Cricinfo
Chasing an easy 236 against New Zealand, Bevan comes in at 4 and soaks up 98 balls (a third of the innings) for 60 runs (much less than a third of the target). Aussie end up having to slog out as the run rate climbs and they lose by 23 runs.
4.
3rd ODI: Australia v South Africa at Melbourne (Docklands), Aug 20, 2000 | Cricket Scorecard | ESPN Cricinfo
This one's a classic Bevan. Chasing 207 off 48 overs, a task so simple you'd almost default, Bevan wastes an astonishing 80 balls for a mere 33 runs. He scored one four in this innings, off 80 balls, and Australia ended up running out of overs 8 runs short.
5.
1st ODI: South Africa v Australia at Durban, Apr 12, 2000 | Cricket Scorecard | ESPN Cricinfo
Limping to 31 runs from a 57 ball innings, Bevan ensures Aussie end up losing with 12 balls to spare. Just imagine if Bevan had scored an extra 20 runs like a normal batsman - probably an Aussie win here.
Bevan seems to be remembered mostly for being not out when matches were won by Aussie. For this reason he's been mythologised to ****. All five of the matches I linked to were lost pretty much entirely by Bevan's poor strike rate and inability to hit boundaries. In all of these matches Aussie would have been better off if Bevan kicked his stumps over first ball and let someone with a higher strike rate bat instead.
Bevan in ODIs is the single most overrated thing in cricket. I'd seriously pick Luke Ronchi in an Oceania ATG side before I picked Bevan.