This is not correct. It was, in fact, "some software bug caused by Ada", in the sense that in most other programming languages, the error that did in fact happen would have been harmless.

For those who are interested, the full report is at http://www-users.math.umn.edu/~arnold//disasters/ariane5rep..... There is no need to "guess" when a fairly detailed public analysis is available, particularly when the issue is one that comes up repeatedly. It is true that the problem was that a horizontal velocity variable ("horizontal bias", BH in the code) overflowed, although it was not the ordinary kind of integer overflow, but rather a floating-point-to-integer-conversion overflow, which does not produce an exception in any commonly-used programming language.

The missing piece of the explanation is that the variable in question was no longer being used at that point in the flight, so if the failure had been allowed to pass silently rather than shutting down the SRI ("inertial reference system"), the rocket would not have been destroyed.

Of course, under some circumstances, allowing variables to have grossly incorrect values in your inertial reference system could have been equally disastrous — that's what you assumed happened. The system was designed in the way it was because the assumption was that such errors would almost surely stem from hardware failures rather than software bugs; perhaps that is a "domain issue caused by a failure in management and testing".

But in some sense, you can argue that any organizational failure is a "failure in management", since management's job is to look to windward and steer the organization clear of failures by any means necessary. But in fact the particular failure in management that happened was for the software to be inadequately thought out, such that one of Ada's hidden pitfalls caused Ariane 5's maiden flight to fail.