I've heard of this before. I don't recall the specifics, but I think it was around the time I was in between jobs about five years ago that I discovered that some companies outsource this HR function. (In fact, it was probably my own: AT&T.) It ensures that only serious inquiries get through and spares the HR department from constantly answering calls to look up and verify payroll information. Come to think of it, if Company A has outsourced payroll, it's not at all surprising that they'd ask someone else to do this, too.

Your employer's advice is correct - if a future employer seeks proof of employment, a copy of one or more recent paystubs should be sufficient. I'm pretty sure that the only bits of information a prospective employer is legally permitted to seek from a former employer are your dates of employment and your last salary. An X-Marker with a PHR certification may be able to verify this.

It is not a reference. For that, you seek the support of someone who can vouch for your performance on the job and you provide that person's name and contact information on your résumé or separate letter of references.

My advice for you in your job search is to be up front about this with any prospective employer. Tell them how to verify your current employment and explain that it is outsourced. Make it easy on them by providing them an alternative without them having to ask you, otherwise they might just skip over you. This way, you present yourself as someone who anticipates problems and finds ways to overcome them before they occur - an excellent trait that many hiring managers look for.

And by the way, it is far easier to land a job when you have a job than to be unemployed and searching. I've been in both situations.

Good luck,
Rex.