I mean, liner notes have errors all the time. And especially for a label that doesn't have any real experience with regular music artists at this point? And for a song where there's no prior indication that Fryer ever had any involvement with it (on any version)? I think it's certainly suspect, at the least.
As for the timeline, when I said early 1989, I meant like January. I think I had gotten that in my head, though, and in reviewing various interviews and articles today, I'm not quite sure from where. I really wish there were some kind of definitive timeline on the production of PHM.
Looking over the articles, though, I think we can put some dates to some of it. For example,
this article says that while Trent was working with Flood in Boston, they went to New York for the Depeche Mode 101 premiere. Apparently, that happened on
April 27, 1989. From that same article, the work on Down In It was first when the TVT deal was signed, with LeBlanc doing some pre-production in New York, and the Sherwood doing all the remixes via mail from London. And it sounds like Fryer came after Down In It, but before Flood, because Fryer was Trent's 2nd choice when Flood was busy with Depeche Mode. After Flood was finished with Depeche Mode is when they did Terrible Lie and HLAH in Boston.
This article also seems to confirm that order.
And then there's another article, but I can't find it at the moment, where he says he had Leblanc do another pass at the mixes for Head Like a Hole.
Edit: Hm,
this article Trent seems to say they did the 2 Flood tracks in Boston first, and then went to London to do the rest of the album.
Edit 2:
Confirmation of the Boston recording dates and Depeche Mode 101 premiere.