Ground control vs. clearance delivery for VFR

My local Delta base (HFD) will contact nearby BDL TRACON and obtain a
squawk code for VFR flight following or traffic advisories. This
service is "advertised" on the ATIS and is requested from ground
control on initial call up by departures. Ground calls you back with
a code and the proper departure frequency, similar to an IFR
clearance.

Last week, I was at a Charlie airport (PVD) during a very quiet
period. Upon calling ground with the usual VFR information, I also
requested a VFR flight following to my destination. This was the
first time I'd tried this outside of HFD. The controller mumbled
something unintellible, along with "since it's slow", and to stand by.
He honored my request and returned with my code and the current
departure frequency. My flight following commenced automatically as I
was handed off to that area's TRACON from the tower.

Should I have asked for this service via the clearance delivery
frequency as in IFR, or was I asking for a service not normally
available? I can't find the answer in the 2007 Jeppesen FAR-AIM.

In hindsight, I'm guessing I should have been on clearance delivery.