300 dpi is what printers generally say to motivate clients to provide images in the highest resolution possible and avoid being liable for a print looking pixelated.
The image is certainly printed at a far lower resolution and downsampled. You will not see the difference between a source image at 300px/inch compared to a 240px/inch. 200px/inch will likely do as well.
If you're working with a small shop they will be able to tell you what is the printer's output resolution. But in most case the people you talk to don't even know what really happens in the shop. You'll end up by increasing the size of your picture which will then be reduced to fit the output settings. I would advice to just import the picture in the layout as it is and export the .pdf with your layout and the let them do their job.
I'm old school (or just old) and resolution really mattered in the 90's when films or prints were scanned to the printer' specs and according to the printing devive's output resolution.
But today you rarely have to scan, you just take pictures at the highest possible resolution and the printer will handle the downsampling without much loss. Your only limitation is the size of the final print when it's really huge or very finely printed. However most mid shelf cameras and an iphone 6 have enough resolution to print large billboards.
If you want to read on the topic here are two articles which explain resolution better than I could: