It not incorrect.
Assault gun where not tank and did not move in close with troops. The fired from a distance where the lack of turret did not make difference. The fire they provided could be direct or indirect.
Stug-E had a gun with high elevation and could fire both direct and indirect fire.
When German where low on tanks and tried to use assault gun as tanks they vehicle failed in the role.
"Assault guns" provide support fire for the infatry to "assault" rather then do the assault themselves.
You are confusing vehicle use. Assault guns were used to give INFANTRY mobile howitzers and bunker busters. This is a very different role than "tanks". In the Assault gun role, the vehicle moves up with the infantry to blow up bunkers and clear soft targets in a direct fire role. But this is different than other forms of self propelled artillery such as the priest, hummel and sexton which were almost exclusively indirect fire units.
Historically, the concept of assault guns was very similar to that of the infantry tank, as both were combat vehicles intended to accompany infantry formations into battle.
Tanks were used as a mobile and independent force not meant to operate with foot infantry. You are correct when you say that assault guns pressed into the tank role were not very effective at this, but you do not seem to understand the actual role of assault guns.
I know it seems intuitive that assault guns would fire from a long distance, but the reality is that operationally they were used in close support with infantry particularly when on the offensive.
Please read up on the actual operational use of the early stug variants and the soviet assault guns like the isu and su76 instead of relying on your intuition.
As a light assault gun, the SU-76M was well-regarded by Soviet infantrymen (in contrast with their own crews). It had more powerful weapons than any previous light tank for close support and communication between infantry and the SU-76M crew was simple due to the open crew compartment.
The important thing to take away is that it was used for CLOSE support, and mouth to mouth communication was used with infantry.