The dangerous storm text does not necessarily infer a supercell, it has also been used for multicells....its purely when they have a spotter report or get such a radar signal that it recieves this statement....usually the prior.
The picture you show there presents in my mind no doubt that this particular storm was a supercell...structure is too well defined to be anything else. I tend to agree with Jimmy's suggestion of LP tendencies though.
As for your 'supercell 2', im a fraction skeptical without seeing any better defined imagery...ive seen bases like that on Multicells...and pulse/air mass thunderies. While it may have sustained supercell like characteristics for a short time period this does not indicate a supercell...rather the development of a short lived mesocyclone.
Only way I know of to obtain better clarification without calling the bureau is to ask yourself the following questions:
1) Relative to the movement of all other isolated storms on that day did this storm move in a different direction without a known wind change? This is usually present on radar imagery (with obvious left/right moving tendencies)
2) Was the storm long lived and isolated, or the northernmost member of a line which sustained for longer than the regular convective cycle (60 mins)?
3) If doppler is available is a mesocyclone discernable (may also be detectable on normal radar in particularly well defined storms)?
4) Is rotation occuring within the cell? (discernable from inflow bands, structural characteristics, production of a clear mesocyclonic tornado etc).
Basically to come out and say a particular storm is a supercell I would expect at least 1,2,4, 1,2,3 or 3,4 to have substantial evidence.
While this is not a be all or end all I do believe its a reasonable method for identifying these storms rather than New South Welshman or Queenslanders for example saying...that is definitely an SC (due to location and conditions), whereas they might not agree in Vic (where the conditions maybe werent as favourable, but a supercell happened).
Nice captures there though.