I cannot reproduce your problem. For me your code works. I've tested it on Windows Vista, 7 and 10. It always installs to C:\Users\Public\MyApp.
Though I do not understand the {drive:{src}}. How does the drive of the Users folder relate to the drive of the installer? You should use the {sd} constant:
[Files]
Source: "MyApp\db.mdf"; DestDir: "{sd}\Users\Public\MyApp"; Flags: ignoreversion
But anyway, to resolve the path to the C:\Users\Public, you can use the PUBLIC environment variable:
[Files]
Source: "MyApp\db.mdf"; DestDir: "{%PUBLIC}\MyApp"; Flags: ignoreversion
It works since Windows Vista.
Alternatively, you can use SHGetKnownFolderPath with FOLDERID_Public. For an example code, see Constant for AppData\LocalLow?
If you need to support even Windows XP, where there is no C:\Users\Public folder or PUBLIC variable, you have to find out, what path your need to use there instead (probably C:\Documents and Settings\All Users), and implement a fallback using a scripted constant:
[Files]
Source: "MyProg.exe"; DestDir: "{code:GetPublicPath}\MyApp"; Flags: ignoreversion
[Code]
function GetPublicPath(Param: string): string;
begin
  Result := GetEnv('PUBLIC');
  if Result <> '' then
  begin
    Log(Format('PUBLIC is "%s"', [Result]));
  end
    else
  begin
    Result := GetEnv('ALLUSERSPROFILE');
    Log(Format('PUBLIC is not set, ALLUSERSPROFILE is "%s"', [Result]));
  end;
end;
And for others, it's worth noting that your need for resolve C:\Users\Public is very specific, related to this question: C++ app MDB in ProgramData copies to user's AppData folder when I dont want it to.
One usually does not want the C:\Users\Public, but C:\Users\Public\Documents (= {commondocs}) or C:\ProgramData aka C:\Users\All Users (= {commonappdata}).