Time Capsule not working with HP Printer, HP support blames Apple

I spent two hours on the phone with an HP technician trying to get my new HP Laserjet Pro P1102w working as a wireless printer using my Time Capsule as the router. He eventually concluded that the Time Capsule is not compatible (at least not in its default configuration) with the HP P1102 laserjet. He asked me to open a support ticket with Apple to ask them how to make that printer work with the Time Capsule. So I'm essentially doing that here.

My Time Capsule is "version 7.7.3." The Router mode is "Off (Bridge Mode)" but that mode does allow me to connect wirelessly to it from my "iMac 5K" to the Time Capsule. My OS is OS X Yosemite v10.10.4. I'm using WPA/WPA2 Personal as the Wireless security protocol. On the router the 2.4 GHz channel is "automatic" and the 5GHz channel is also automatic. I think the HP technician said it might work better with HP printers on channels 6 or 11. I have no idea what that means. He didn't change those channels on the Time Capsule.

I told him I thought HP should document the requirements to make their printer work with Time Capsule, but he thought it was Apple's responsibility to document how to make it work. Obviously this community will be filled with pro-Apple people so we aren't going to agree with him here.

In any case, we gotta give credit to HP for taking two hours out of their day to help me get a $90 laser printer to work. And I should add that most of the time was spent reviewing all the settings on the printer, so from HP's perspective, we tried every option on that printer and so there's probably nothing more on the printer that we could have tried.

Eventually I was able to get the printer to work by changing the printer to use my ISP's wireless router instead of my Time Capsule (I have the Time Capsule in series with my ISP's router), but I'm trying to use TC because it was much more reliable when I compared it to the ISP's router. I don't want to use my ISP's router. Can anyone help? Bottom line: why won't an HP P1102w work with Time Capsule even after spending two hours with HP support?