Good point with accessing that one setting through the ApplicationAddIn object representing the iLogic add-in @Raider_71.
Since 'iLogic' is an add-in within Inventor, we can find the ApplicationAddIn object representing it, then get the value of its ApplicationAddIn.Automation property to a variable, as an Object. Then that variable can essentially be used the same was as the IiLogicAutomation Interface, which is what we get from the [iLogicVb.Automation'] code phrase within an iLogic rule.
The other two similar properties of that object are: RulesEnabled & SilentOperation.
There are actually at least 3 different places where we have control over a setting named 'SilentOperation'. One is just under the main Inventor.Application object (Application.SilentOperation). One is under that main iLogic Automation object. And one is for each individual iLogicRule object (iLogicRule.SilentOperation).
Similar for the other settings controlling rules running when events happen. There are settings for that which can only be set/changed manually, which will override the authority (on the security side) of any settings that we can change by code. Those settings can be reached by going to the Tools tab, Options panel, clicking on the 'iLogic Configuration' tool to open that dialog. Then clicking on the [Security Options] button within that dialog, which opens another small pop-up labeled 'iLogic Security'. The settings you set there will override any similar sounding ones that you can access or change by code, for security reasons. Then there are the settings mentioned above, just under the main iLogic add-in's Automation object.

Then there are similar settings for each individual iLogicRule object.

iLogicRule.AutomaticOnParamChange
iLogicRule.FireDependentImmediately
iLogicRule.IsActive
iLogicRule.SilentOperation
(no code based access to the option named 'Straight VB Code', as far as I can tell)
And besides the strategy of using the ApplicationAddIn.Automation object to get partial access to some of those settings, we can also 'pass' the uniquely iLogic 'RuleObject' named "iLogicVb" (which is the ILowLevelSupport Interface) out to our external resources (such as a Class) for temporary use, if needed, either through an 'input parameter' of a method, or by setting it as the value of a Public property of the external resource. This can give an otherwise purely Inventor API or vb.net based code resource access to uniquely iLogic resources.
Wesley Crihfield

(Not an Autodesk Employee)