The SRD conflates the
Player's Handbook Glossary definition of
invisible (pages 309-310) and the
Dungeon Master's Guide Glossary treatment of
invisibility (pages 295-296). However, the original source locations do matter here in terms of adjudicating disagreements.
Errata Rule: Primary Sources
When you find a disagreement between two D&D® rules sources, unless an official errata file says otherwise, the primary source is correct. One example of a primary/secondary source is text taking precedence over a table entry. An individual spell description takes precedence when the short description in the beginning of the spells chapter disagrees.
Another example of primary vs. secondary sources involves book and topic precedence. The
Player's Handbook, for example, gives all the rules for playing the game, for playing PC races, and for using base class descriptions. If you find something on one of those topics from the
Dungeon Master's Guide or the
Monster Manual that disagrees with the
Player's Handbook, you should assume the
Player's Handbook is the primary source. The
Dungeon Master's Guide is the primary source for topics such as magic item descriptions, special material construction rules, and so on. The
Monster Manual is the primary source for monster descriptions, templates, and supernatural, extraordinary, and spell-like abilities.
Dealing with invisible opponents is a part of rules for playing the game. The
Dungeon Master's Guide is where the "grope about to find an invisible creature" rules are. The
DMG can supplement those
PH rules, but it can't override them, or establish a conflicting default.