They might not even be trying to "stretch" it (a large company could give a crap about the float on an indie consulting invoice); they might just run accounts payable on a state machine in which the part that elapses a timer hasn't started yet. There might be all manner of reasonable reasons for doing it that way; for instance, if they accidentally release payment early, they may screw up projects by blowing expectations.
In any case, yeah: some of your best clients will do a terrible job paying you on time. 'slife in the big leagues.
I once worked in a bank doing tech support and occasionally fixed a few things in the sealed-off internal finance room. The place was littered with red final notices - including utility, phones, everything. As a bank they could easily put to use any extra cash they had, so the official policy was to pay everything late. No doubt everyone knew they would pay eventually, but when you're big you don't have to.
When I freelanced one of my customers moved the accounting to SAP, which had the unfortunate consequence that they didn't pay me for four month.
It was, however, a reputable, well known firm and I had no reason to believe that they where playing games or trying to bullshit me.
I was right and got payed in full when the glitches got ironed out. Nevertheless, it was a tad annoying and part of the perils of a freelancer, I guess. Thankfully, while being persistent with their accounting department I never blew up and always stayed civil.
Very much second that setting up the invoicing for a new supplier can take time, especially at multinationals or other large firms. I can understand this due to the fact, that procurement is one of the most sensitive areas when it comes to fraud and dodgy invoicing. Thus firms set up a lot of safeguards before actual money flows.