I find it highly plausible that a member of on-board staff would say this ticket can't be used that way (either because they read something into the Railcard restrictions that isn't there, or because they disbelieve the passenger when they say they started short, or a bit of both).
In my humble opinion, though, anyone who says this ticket can't be used at all on a train that departs the origin before 10am is wrong. It's uncontroversial that starting short is permitted. The 10am restriction applies to the use of the Railcard i.e. travelling on a discounted ticket. If the train departs the origin on the ticket at 9.40 and departs the station where you start short at 10am, the time you started travelling on the ticket is 10am.
I wouldn't recommend anyone goes out of their way to test this or to draw attention to the fact they're starting short in circumstances like this, though. I think it's completely legitimate and I reckon (though obviously can't be sure) that any serious dispute about this would ultimately be resolved in favour of the passenger, but the rail industry might perceive that if this interpretation became official and widely known then it would leave them vulnerable to people short-faring and then pretending they'd started short after 10am when challenged. It may be one of those things that's best left ambiguous and used circumspectly. If the TOCs perceive the rules don't favour them they may try to get them changed.
If anyone wants to split tickets (e.g. a non-discounted ticket to cover part of the journey before 10am and a discounted ticket to cover the remainder) then I think that's much more obviously legitimate and easier, if required, to demonstrate that you hadn't used the discounted ticket to travel before 10am. But again, there's no need to draw attention to it unnecessarily - the ticket inspector only needs to see the ticket you're using at the time.
