Good question and there's no right answer just now. The Rochester criteria (or Boston or Philly) only looked at infants 0-4 weeks, where everyone (currently) agrees the full work up is necessary. Beyond 4 weeks it can get controversial. And really where do you draw the line? What's the difference between a 33 day old and a 29 day old? Even a six week old I may not tap if they have fever and good follow up, but a five week old I probably will. If you had a cellulitis on a 3 months old who was vaccinated I probably wouldn't do an LP, but if he were 7 weeks? I might, it depends. I've found that I do fewer taps now than when I started and thought that EVERYONE needed a needle in their back.
Now, as to tapping when there is another obvious source. The main concern is that children don't opsonize very well. If there's an infection in one place, there's a risk that it will/has easily spread to other places. Think of your old nursing home grandma who has urosepsis. The most extensive data is on UTIs and the general feeling is that even with another source, like a URI, if a kid is febrile, they have around a 5% (ish) chance of having a concomitant UTI.
There was one study that looked at RSV positive infants and the rate of sepsis and they didn't find any incidence of meningitis but 6% also had UTIs. But you cannot extrapolate that data and say that the risk of meningitis is zero. So in general I check a lot of urines for infection.
Part of it also has to do with dispo. I'd have a lower threshold to admit a younger kid for pneumonia or cellulitis, and if I'm admitting them, then I'd probably talk to their pediatrician or the hospitalist and ask what they'd like to do. I doubt that anyone will ever fault you for tapping a kid automatically, and if you're sending them home consider the tap. What you don't want to get into is a partially treated meningitis because it's such a pain for everyone to deal with. You send the kid home on an antibiotic, then two days into his treatment he starts getting sicker and you wonder if you miss something.
So talk to your peds people, make sure they have good follow up, and you could go either way. When in doubt, tap, especially if you think parents are unreliable. Missing meningitis is a big litigation deal in peds. That was long, but maybe not so helpful.