Okay, replaying the singleplayer, I think it went like this:
Orks invade planet in a massive WAAAAAGH, target the titan manufactorum. PDF is utterly crushed, and everyone gets murdered to hell over a week or more, but while most of the local defenders are dead, the Orks haven't broken through the automated defenses and the manufactorum itself hasn't been breached. Techpriests and Skitarii probably went to meet them head on (or supporting the PDF) and got overwhelmed by sheer numbers (when the Ultramarines get there, it's already been at least a week, and it's still raining roks from the sky, so their numbers are rather daunting). Guard reinforcements nearby are diverted to lend a hand, but the orks have turned the very considerable defenses against them, so only a handful break through and get stuck in a war of attrition for at least a few days (I think lt mira mentions it's been more than a week as well - the intro itself says 9 days but the ingame dialog makes it sound like more), which they are slowly losing.
For all we know there may be Titans at the other manufactorums on the planet (in the intro you can see that Ajakis is the only one really being torn apart), but I can't imagine you would be able to use them without obliterating the crap out of the place (although they could probably blow the crap out of the defense guns... Or maybe the defense guns pose too much of a risk to a Titan since they've been shown to easily cleave starships in half).
Then there's also the Princeps and his crew holed up somewhere in the manufactorum, which is probably where the surviving Skitarii and Techpriests would be (and they'd just hold down the fort in the manufactorum while the guard fights outside). There's also a chance that a number of Techpriests and Skitarii were killed by Nemeroth when he took over the Inquisitor (since he mentions in the audio logs that they were involved in his research).
It seems somewhat plausible I guess; unlikely, but eh, it's 40k, stranger things have happened. I'm still missing like 11 skulls though (mostly the later ones) so maybe there's more bits and bobs in there.