Of course, and as always when using Delphi, there is a workaround to this problem. The workaround is called the "protected hack", or "accessing protected members of a component".

THackDBGrid - OnClick aware

When hacking the DBGrid to expose the OnClick event handler you *only* need to create a subclass of a TDBGrid inside the unit where you want to use the hacked grid, and assign an OnClick handling procedure to the hacked grid's OnClick property.

In Delphi code, the above would look like:

uses
  Windows, Messages, ..., Grids, DBGrids, ... ;

type THackDBGrid = class(TDBGrid);

type
  TForm1 = class(TForm)
    DBGrid1: TDBGrid;
....

Inside the Form1's OnCreate handler add the following:

procedure TForm1.FormCreate(Sender: TObject);
begin
  THackDBGrid(DBGrid1).OnClick:=DBGrid1OnClick;
end;

The DBGrid1OnClick (declared in the private part of the Form1's declaration) procedure might look like:

...
type
  TForm1 = class(TForm)
    DBGrid1: TDBGrid;
...
private
   procedure DBGrid1OnClick(Sender : TObject);
...
    
procedure TForm1.DBGrid1OnClick(Sender : TObject);
begin
  ShowMessage('Clicked on the DBGrid1');
end;

That's all - the DBGrid1 now responds to its OnClick event.

THackDBGrid ... [csClickEvents] in ControlStyle

To finish our task of OnClick-enabling the DBGrid we need to make sure the hacked grid can receive and respond to mouse clicks (in an ordinary Windows fashion) - by adding the csClickEvents flag to the ControlStyle property.
To finish the job, alter the OnCreate handler of the Form1 to look like:

procedure TForm1.FormCreate(Sender: TObject);
begin
 THackDBGrid(dbgrid1).ControlStyle :=  
 THackDBGrid(dbgrid1).ControlStyle + [csClickEvents];
 
 THackDBGrid(DBGrid1).OnClick:=DBGrid1OnClick;
end;

And we are finished. Note that you can expose the OnDblClick (double click) for the DBGrid1 in the same way.

Warning!