Your dealer has made a misdiagnosis...or at least a mistaken correlation. Except at the moment of starting, HIDs generally take less juice than the OEM lights. Your problems are probably coincidental. Your charging system and your battery need to be tested. You can do these tests yourself, after a fashion. Before testing, check that the battery connections, at the battery, not the jump start terminals, are free of oxidation/corrosion and are tight. Poor battery connections prevent proper charging.
Charging System:
The system should read 13-14 volts with the engine running at 4000 rpm. If not, have the charging system thoroughly tested by a dealer. Note that low rpm operation can be ineffective in recharging the battery with a large accessory load.
Battery ability to take a charge:
If the charging system checks out, charge the battery on a maintainer (if possible) or by taking a long ride. A good battery should read 13 or more volts immediately after fully charging. If it reads less than 12.7, it needs to be replaced.
Battery ability to hold a charge:
After charging, let the battery sit off the charger for several hours to overnight. It should read 12.7 volts or higher in the morning. If less, charge it again and disconnect it overnight, then test again. If it is OK then, parasitic losses in the electrical system are pulling it down, such as from continuously powered accessories or component faullts. If it is still low after sitting disconnected, the battery needs to be replaced.
Battery load test:
A crude load test can be run by holding the throttle wide open to prevent starting, then taking a reading while cranking. It should read 10.0 volts or greater. If less, replace the battery or have a dealer confirm with a proper load test.
I suspect you have a bad battery or connections if you are not chronically running at low (below 4000) rpm.