Not the most helpful answer, but I think this is just a bit of a garbled claim in WP. A couple of years ago it stated:
The island was one of 33 emergency landing sites worldwide for the NASA Space Shuttle. None of these facilities were ever used throughout the life of the shuttle program.
The mention of Apollo was added with a slightly confusing edit summary a few months back. I've now taken it back out...
More prosaically, as @PearsonArtPhoto notes, no Apollo flights ever used the Indian Ocean area for splashdowns. However, it was identified as a potential backup landing area. The Apollo 10 (p 23), and 11 (p 64) press kits identify "planned recovery lines" for lunar flights in the West Pacific, Mid-Pacific, East Pacific, two in the North and South Atlantic, and one in the Indian Ocean around 65E. For each mission, it seems that the Mid-Pacific was designated as primary, and one or two as alternates. By Apollo 12 (p 27), they were not listing details of recovery lines other than the backup.
There is a note about aircraft positioning which suggests they were all provisionally covered in some capacity - the Apollo 10, 11, and 12 missions all mention a C-130 based on Mauritius. This presumably meant that there was a minimal level of cover for the Indian Ocean landing area, but not operating out of Diego Garcia. This strongly suggests it had no role to play in the Apollo recovery plans.
By Apollo 13 (p 44), they had cut down the number of support aircraft to five bases, versus seven or eight before, and there was no longer an Indian Ocean presence at all, just west Pacific and Atlantic. The same was true for Apollo 14 and 15 (when it went down to four bases), and for 16 and 17 they didn't even mention it. It looks like the Indian Ocean was seen as a possible contingency early on, and abandoned as they grew more confident. But even at that point, Diego Garcia does not seem to have been used at all.