Building Custom Eagle part with bad documentation
No, the closest grid position is not automatically good enough for pins or other features.  The fundamental realization should be that you don't have to place features on the existing grid.


You can temporarily change the grid to something that works for the needed features
You can individually select the features and edit their actual coordinates to the correct location irrespective of the grid


Also note that you can temporarily switch the units between inches and mm to fit whatever your documentation is in.

Finally, if doing PCB design you really should have the part and a cheap pair of digital calipers in hand for double checking.  If you doubt the result, print it out at 100% scale (put a known diameter box around it which you can measure to verify the printer scaling) and set the part on the paper.

In your specific case, the pins of the part will fit on a 100 mil / 2.54 mm grid, however the housing outline may not.  In that case you'd probably be happiest leaving the pins on grid, and adjusting coordinates of the outline corners numerically

It's also worth noting that you've used square pads for all pins.  Where practically workable, it's something of a tradition to use a square pad for pin 1 and round pads for the others, so that they may be readily distinguished without reference to silkscreen.